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Physics Condensed Matter Strongly Correlated Electrons

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Friday 11 September

Strongly Correlated Electrons · Cross-listed from hep-th

Bootstrapping currents and stress tensors in 3d CFTs

Vasiliy Dommes, Rajeev S. Erramilli, Colum Flynn et al. (+5 more)

We perform a numerical conformal bootstrap study of the mixed system of correlation functions involving a spin-1 $\mathrm{U}(1)$ current $J$ and the stress-energy tensor $T$ in parity-preserving 3d CFTs. We find universal bounds on the stress-tensor two-point function $c_T$, which numerically reproduce the conformal collider bounds on $\langle JJT\rangle$ and $\langle TTT\rangle$, as well as bounds on the leading parity-even and parity-odd scalar operator dimensions. Under mild assumptions, we determine the values of the $\langle JJT\rangle$ and $\langle TTT\rangle$ three-point functions in the $\mathrm{O}(2)$ vector model. The $\langle TTT\rangle$ result is new and $\langle JJT\rangle$ is consistent with a previous result in the literature.
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All authors Vasiliy Dommes, Rajeev S. Erramilli, Colum Flynn, Alexandre Homrich, Petr Kravchuk, David Poland, David Simmons-Duffin, George Yuzhe Zhou

Strongly Correlated Electrons

Magnon-induced hybridization brightens excitons in ferromagnetic semiconductors

Man-Yat Chu and Mona Berciu

Excitons in magnetic semiconductors have energies and spin structures that are sensitive to the underlying magnetic order. We study this coupling in a minimal one-dimensional lattice model of a conduction electron and a valence hole moving in a ferromagnetic background of localized quantum spins, treating the electron, the hole, and the magnon(s) as explicitly resolved degrees of freedom. At zero temperature, spin conservation closes the relevant Hilbert subspaces at the one- or two-magnon level, so the model can be solved essentially exactly with a real-space Green's function method. Comparison against a frozen-spin approximation in which the local moments are replaced by their ordered values identifies which effects are due to emission and absorption of quantum magnons. A frozen background already lifts the spin degeneracy of the exciton and, if the two carriers couple with different strengths to the local moments, it mixes the singlet with the spin-zero triplet exciton. The emission and absorption of quantum magnons goes qualitatively further: it splits and shifts the exciton energies nonlinearly in the exchange coupling even when all frozen-spin effects vanish; for carriers with unequal hopping integrals, it hybridizes the singlet and spin-zero triplet excitons, thereby brightening the dark triplet; and it increases the exciton radius, which in turn enhances the magnon dressing by removing an on-site cancellation. These quantum effects are therefore strongest for extended, Wannier-like excitons, which is precisely the regime that is commonly modeled assuming a static (frozen-spin) magnetic order.
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Strongly Correlated Electrons

2D Weak Localization in Trilayer Ruddelsden-Popper Nickelates

Hyo-Bin Ahn, Xinglong Chen, Yu Zhang et al. (+5 more)

Ruddlesden-Popper (RP) nickelates superconduct when pressure suppresses intertwined charge- and spin-density waves. Here, we employ measurements of quantum corrections to magnetoconductivity as a probe of the dimensionality, phase coherence, and scattering mechanisms of the underlying single crystal trilayer RP nickelate Pr4Ni3O10 and La4Ni3O10. We observe signatures of 2D Weak Localization (WL), implying that the in-plane electron transport is in the quantum diffusive regime, while the out-of-plane transport is incoherent, and the electronic ground state is a quasi-2D disordered Fermi liquid. Application of pressure up to 3 GPa continuously suppresses signatures of WL, potentially signaling a 2D/3D dimensional crossover and an eventual pressure-driven transition into a superconductor.
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All authors Hyo-Bin Ahn, Xinglong Chen, Yu Zhang, Hong Zheng, Michael R. Norman, J. F. Mitchell, Daniel Phelan, Ulrich Welp

Strongly Correlated Electrons · Cross-listed from quant-ph

Thermal robustness of sensing quantum phases of matter via qubit probes

Sambunath Das, Hari Kumar Yadalam, Mark T. Mitchison et al. (+1 more)

We study the effect of temperature on the ability of a qubit probe to distinguish between different phases in strongly correlated systems. Now to this end, we investigate a spin-1/2 Heisenberg XXZ chain coupled to a qubit probe via a pure dephasing interaction. At zero temperature, as reported previously, the decoherence dynamics exhibit different behavior in the gapped and gapless phases of the chain, with characteristic strong oscillations in the gapped phase and monotonic decay in the gapless phase. These oscillations decay much more slowly than expected with rising temperature in the gapped phase and their remnants are still visible at infinite temperature. In the gapless phase at low temperatures, using Luttinger liquid theory, we predict that the coherence exhibits asymptotic exponential decay in time, with the decay rate sensitive to the sign of the anisotropy parameter. We conclude that probe dynamics continue to carry information about the chain even at finite, reasonably small temperatures, positioning qubit probes as sensitive and robust detectors for quantum phases of correlated spin systems.
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All authors Sambunath Das, Hari Kumar Yadalam, Mark T. Mitchison, Katarzyna Roszak

Strongly Correlated Electrons

Orbital Hall effect and orbital altermagnetism in even- and odd-parity-wave magnetic Lieb lattices

Börge Göbel, Ersoy Şaş{\i}oğlu and Samir Lounis

Altermagnets combine compensated antiferromagnetic order with ferromagnet-like signatures such as spin-polarized bands and, under appropriate conditions, an anomalous Hall response. Their characteristic momentum-dependent spin splitting originates from the interplay of magnetic order and crystal structure and therefore does not require spin-orbit coupling (SOC), whereas the anomalous Hall effect relies on SOC. This raises the question whether the ferromagnet-like transport character of altermagnets can manifest already in the nonrelativistic limit. Here, we investigate the transport of orbital angular momentum in magnetic Lieb lattices. We show that a collinear antiferromagnetic texture realizes a d-wave altermagnetic state and simultaneously generates an orbital Hall effect, both in the complete absence of SOC. In this nonrelativistic limit, the orbital Hall response closely resembles that of the corresponding ferromagnet. When SOC is included, the orbital Hall effect is accompanied by a spin Hall response, while the altermagnetic spin texture acquires a corresponding orbital texture, realizing orbital altermagnetism. In contrast, an anomalous, or crystal, Hall effect requires SOC and is additionally subject to crystal-symmetry constraints. We extend the analysis from d-wave altermagnetism to odd-parity p-wave magnetism, where the orbital Hall effect becomes anisotropic and the orbital conductivity tensor develops a symmetric transverse component analogous to the planar Hall response in charge transport. Our results establish the orbital Hall effect as a nonrelativistic transport manifestation of the close relation between altermagnets and ferromagnets and extend this connection to unconventional magnetic orders beyond altermagnetism.
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Strongly Correlated Electrons

Spin splitting without symmetry: a nearly compensated ferrimagnet and the origin of altermagnetism

Joo Yull Rhee

The spin splitting of collinear altermagnets is usually attributed to the crystal symmetry relating the opposite-spin sublattices — a rotation or mirror in place of the translation or inversion of a conventional antiferromagnet. We show that this symmetry organizes the splitting but does not produce it; its origin is the anisotropic arrangement of the magnetic orbitals and their ligands, which also fixes the symmetry itself. Two results establish this. A triclinic ($P1$) \ce{Mn} oxide, a fully compensated ferrimagnet whose two inequivalent sublattices are related by no symmetry, is spin split throughout the Brillouin zone; repositioning the same ligands, atom for atom, to restore an inversion centre relating the two metal sites collapses the splitting to a residual two orders of magnitude smaller, so the splitting follows from the arrangement rather than the symmetry. Symmetry, we show formally, can only ever reverse or forbid a splitting that already exists: it cannot create one between sublattices an arrangement has left electronically identical, nor where the underlying orbitals carry no anisotropy to arrange in the first place. Organizing the analysis through an operation-resolved symmetry hierarchy and reading the crystal classes as a single axis, the enforced nodal planes fall from two to one to zero across the orthorhombic, monoclinic, and triclinic classes while the arrangement-generated splitting persists to the base. The altermagnet and the fully compensated ferrimagnet are thus the two ends of one axis — the same splitting, organized by symmetry at one end and unorganized at the other — and the search for compensated spin-split magnets is a search over orbital arrangements rather than symmetry labels.
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Strongly Correlated Electrons

Chiral Valence-Bond Solid and Chiral Triplons

Shinnosuke Koyama and Kazumasa Hattori

We propose a chiral valence-bond solid (VBS) state that spontaneously breaks inversion and mirror symmetries. It is characterized by a finite electric toroidal (ET) monopole, whose sign distinguishes the two enantiomorphic states. Using a spin-lattice model with Dzyaloshinskii-Moriya interactions, we show that the chiral VBS produces spin-split triplon bands with enantiomer-dependent spin textures governed by its ET monopole. Under a temperature gradient, these spin textures generate a net spin response whose sign is tied to the handedness of the VBS. More importantly, we show that the imaginary off-diagonal components of the dynamical spin structure factor change sign between the two enantiomers, providing a direct neutron-scattering probe of the selected handedness. These results establish a route to spontaneous chirality in a valence-bond system and to its direct detection through magnetic excitations.
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Strongly Correlated Electrons

Diversifying time evolution of matrix product states using BUGs

Kornél Kapás, Dominik Sulz, Charlotte Verhoeven et al. (+3 more)

Time evolution of tensor-network states is a central tool for studying nonequilibrium dynamics in strongly correlated quantum systems. In the past decade, using the time-dependent variational principle (TDVP) discretized by projector-splitting has become the gold standard for evolving matrix product states (MPS) with long-range Hamiltonians. More recently, a conceptually different class of discretizations of the TDVP, the class of Basis Update and Galerkin (BUG) integrators, has been developed within the framework of dynamical low-rank approximation, offering an alternative, more flexible approach. In this work, we formulate two BUG integrators explicitly for MPS. The BUG integrators result in "single-site" MPS integrators that are robust with respect to small singular values, avoid backward-in-time substeps, and naturally allow for the adaptive choice of bond dimensions. We consider the augmented BUG integrator of first order and the midpoint BUG integrator of second order and clarify their relation to the projector-splitting discretization of the TDVP. Using representative models of strongly correlated quantum systems, like the XY spin model with long-range interaction and two-dimensional lattice models of fermions and spins of various lengths, we perform a systematic numerical comparison between BUG and projector-splitting time discretizations of the continuous-time TDVP, focusing on scalability, numerical complexity, and accuracy. We find that BUG integrators, due to their reduced numerical cost and the flexibility of the concept, provide a competitive and, in certain regimes, advantageous alternative to the well-established time-stepping by projector-splitting in TDVP, especially in models with large local dimensions, and in cases where observables are extracted with high temporal resolution.
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All authors Kornél Kapás, Dominik Sulz, Charlotte Verhoeven, Miklós Antal Werner, Örs Legeza, Christian Lubich

Strongly Correlated Electrons · Cross-listed from hep-th

Superstrip Algebras and Nonperturbative Spectra in Fermionic Theories

Jin Chen, Zhihao Duan, Qiang Jia et al. (+1 more)

This is an extended version of arXiv:2511.22129. We develop a general construction of the superstrip algebra $\mathbf{sStr}_{\mathscr C}(\mathcal M)$, the fermionic counterpart of the strip algebra, for a gapped $(1+1)$-dimensional system with a fermionic superfusion category $\mathscr C$ and the vacuum structure described by the supermodule category $\mathcal M$. As illustrations, we work out the superstrip algebra for two simple examples: the fermionic variant of the Fibonacci fusion category and the q-type $\mathbb{Z}_2$ symmetry. We then apply the framework to the gapped IR phases of the $\mathcal N=2$ and $\mathcal N=1$ superconformal minimal models deformed by their least relevant operator and compute the Witten indices. We explain how the particle and soliton spectra, together with their fermion parity, are organized into representations of the corresponding superstrip algebras. A mixed 't Hooft anomaly between the spontaneously broken symmetry and the unbroken fermion parity $(-1)^F$ further forces each $\mathcal N =2$ soliton to carry a fractional fermion number. Finally, we set up the boundary SymTFT for fermionic systems and reproduce the results in several examples studied in this paper.
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All authors Jin Chen, Zhihao Duan, Qiang Jia, Sungjay Lee

Strongly Correlated Electrons · Cross-listed from hep-th

Conformal defects of general dimensions at finite temperature

Yucheng Li, Haruki Nakayama and Tatsuma Nishioka

We consider defect conformal field theories (DCFTs) at finite temperature, where a $p$-dimensional conformal defect wraps the thermal circle. Extending the previous study of line defects to defects of general dimensions, we determine the general forms of the thermal one-point functions of bulk scalars, conserved currents and the stress tensor by imposing the residual symmetry and the conservation laws. The low temperature expansion of the thermal one-point functions is shown to be reproduced by the bulk-defect operator expansion, allowing us to read off the thermal one-point coefficients of defect operators. We examine the general results in four classes of examples with free bulk theories: the trivial defect, free scalar and fermion theories with a boundary, the free scalar theory with a localized $\phi$ deformation in $d=2\,p+2$ dimensions and the free $\mathrm{O}(N)$ model with a localized $\phi^2$ deformation in $d=p+2-\epsilon$ dimensions. In the last example with $\epsilon = 1$, where the defect becomes an interface, we find that the thermal one-point functions coincide with those of the free scalar theory with the Dirichlet boundary condition, in accordance with the conjectured factorization of an interface CFT into two decoupled boundary CFTs.
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Strongly Correlated Electrons

Nonequilibrium Broken-Symmetry States from Retained Observables

Sankha Subhra Bakshi and Gia-Wei Chern

In equilibrium, broken-symmetry states are selected by the competition between energy and entropy. Out of equilibrium, slowly relaxing observables retain information about the preparation and may reshape this competition, allowing orders that are not thermally favored. Identifying such states ordinarily requires following slow, protocol-dependent dynamics. Here we recast this dynamical selection as a static constrained variational problem. A small set of experimentally measurable or numerically accessible quantities-particle number, energy, and slow observables-defines a constraint space. The underlying dynamics determines where the system lies in this space, while entropy maximization over both quasiparticle occupations and a prescribed class of candidate orders determines which order is selected. Restricting the variational states to the Gaussian manifold yields a computationally inexpensive constrained Hartree-Fock implementation. For photoexcited Hubbard models, the approach reproduces the long-time TDHF suppression of square-lattice antiferromagnetism and identifies incommensurate spiral order in place of the equilibrium $120^\circ$ state on the triangular lattice. For a continuously driven ferromagnetic double-exchange model, evaluating the constrained order map at the stationary NESS energy reveals a restricted region in which Neel order is favored. The framework therefore turns the search for nonequilibrium broken-symmetry states into a practical static screening problem, without requiring simulations of every preparation protocol.
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Strongly Correlated Electrons

Magnetically activated optical visibility of many-body excitons in NiPS$_3$

Shuta Matsuura, Shohei Imai and Naoto Tsuji

NiPS$_3$ is a layered van der Waals magnet that provides a unique platform for exploring the interplay between excitons and magnetic order. In its antiferromagnetic phase, strong many-body interactions give rise to a many-body exciton, which manifests itself as an exceptionally sharp resonance near $1.47 \, \mathrm{eV}$ in optical absorption spectra and photoluminescence. Previous theoretical studies have assigned the local ground state and the many-body exciton to spin-triplet and spin-singlet states, respectively, both with even parity. This picture, however, cannot account for the observed optical visibility of the many-body exciton because one-photon transitions between these states are forbidden by spin and parity selection rules. Here, using group-theoretical analysis and exact diagonalization of single- and two-cluster models, we show that zigzag antiferromagnetic order breaks the relevant symmetries and activates the otherwise forbidden transition. We further find that trigonal distortion of the local ligand environment and the inter-cluster exchange interaction relax additional spatial and spin constraints on the transition, producing an exciton signal in the optical conductivity that is distinguishable from the spectral background. These results provide a microscopic explanation for the optical visibility of the many-body exciton and its connection to antiferromagnetic order in NiPS$_3$.
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Strongly Correlated Electrons · Cross-listed from cond-mat.mtrl-sci

Observation of topological surface phonons in diamond with nonlinear optics

Qi Wang, Xinyi Liu, Xinyue Sheng et al. (+8 more)

Topological quantum states in electronic systems have profoundly transformed the understanding of phases of matter. Recent theories predict novel vibrational topological quantum states, i.e., topological phonons in various solids. However, this paradigm is yet to be established due to the lack of convincing experimental verification of topological surface phonons—a hallmark signature of topological phonon states. Here, we report the discovery of topological surface phonons in diamond using sum-frequency spectroscopy—a nonlinear optical spectroscopy capable of probing surface phonons with high sensitivity. Diamond, known for exceptional hardness and thermal transport, is unveiled as a phonon topological semimetal hosting topological nodal-lines and nexus triple points in the bulk. With consistent theory and experiments, we uncover the resultant topological surface phonons on diamond (111) and (100) surfaces. Moreover, by chemically modifying these surfaces, we reveal the disorder effect on topological surface phonons. These findings pave the way for bridging two fundamental domains: quantum topology and lattice dynamics, besides having important implications on diamond-based devices and functional interfaces.
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All authors Qi Wang, Xinyi Liu, Xinyue Sheng, Zhi-Kang Lin, Xiaowei Lu, Xiaosheng Yang, Peining Li, Yizhou Liu, Chang-Hui Li, Wei-Tao Liu, Jian-Hua Jiang

Strongly Correlated Electrons · Cross-listed from cond-mat.mtrl-sci

Revealing Hidden Inversion Symmetry Breaking in ZrTe$_5$ via Phonon-Assisted Heterodyne Amplification

S. J. Li, J. H. Huang, H. Y. Wu et al. (+13 more)

ZrTe$_5$ is a sensitive topological material where small perturbations can alter its electronic structure. Its equilibrium crystal structure has been widely regarded as centrosymmetric, while recent experiments have raised the possibility of inversion-symmetry breaking. Here we probe this hidden symmetry lowering using nonlinear optical spectroscopy. Although conventional second-harmonic generation does not resolve an equilibrium symmetry-breaking signal, terahertz-field-induced second-harmonic generation (TFISH) reveals it through phonon-assisted heterodyne amplification. A coherently driven infrared-active phonon acts as a local oscillator for the vanishingly weak second-order susceptibility $\chi^{(2)}$, converting an otherwise undetectable symmetry-breaking response into a phonon-frequency modulation of the TFISH signal. The field-linear scaling of this modulation demonstrates $\chi^{(2)}$ is an equilibrium susceptibility rather than a response induced by the THz field. Polarization- and temperature-dependent measurements identify a bulk polar distortion along the crystallographic $a$ axis that persists to room temperature, while the $c$ axis remains nonpolar. These results provide direct optical evidence for equilibrium inversion-symmetry breaking in bulk ZrTe$_5$ and establish a structural constraint for understanding its electronic and topological properties.
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All authors S. J. Li, J. H. Huang, H. Y. Wu, S. P. Zheng, C. J. Kong, B. Xu, H. Wang, T. Dong, L. Yue, D. Wu, Y. Wan, Z. L. Li, X. B. Wang, S. J. Zhang, N. L. Wang, Y. T. Li

Strongly Correlated Electrons · Cross-listed from cond-mat.supr-con

Emergent magnetism, heavy electrons and pressure-induced reentrant superconductivity in the iron substituted 4d transition-metal sulfides

Yalei Huang, Lu Xin, Na Zuo et al. (+16 more)

Superconductivity emerging from or in the vicinity of magnetic states is generally considered to be mediated by spin fluctuations and thus lies beyond the scope of conventional electron-phonon coupled BCS framework. Here we report the emergence of novel ferromagnetism in the d-electron rhodium sulfide Rh17S15 superconductor, characterized by an enhanced Sommerfeld coefficient {\gamma} arising from the flat topological band and many-body correlations. We further demonstrate that the ferromagnetism can be tuned via Fe substitution at the Rh sites, leading to a spin glass ground state induced by the competing ferromagnetic and antiferromagnetic exchange interactions. Fe doping results in a further enhancement of both the {\gamma} and electron effective masses. At a doping level of x = 0.67 in Rh17-xFexS15, {\gamma} reaches 312 mJ mol-1K-2, second only to the well-documented d-electron heavy-fermion material LiV2O4. Furthermore, upon applying pressure, superconductivity is first suppressed; under high pressures, however, we observe the reentrant superconductivity in both pristine and Fe-doped samples. Our results not only demonstrate the unusual magnetic states and possible heavy-fermion features in these frustration-free, d-based superconductors, but also suggest that the superconductivity in this system is likely mediated by the intrinsic spin fluctuations and may thus be unconventional.
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All authors Yalei Huang, Lu Xin, Na Zuo, Bin Li, Wei Zhou, Dhanarajagopal Alltrin, Boning Yu, Haiyang Yang, Bin Qian, Wen-Chin Lin, Raman Sankar, Michael Smidman, Xiangzhuo Xing, Chunqiang Xu, Xiaobing Liu, Jianhui Dai, Dong Qian, Shiyan Li, Xiaofeng Xu

Thursday 10 September

Strongly Correlated Electrons

Geometric Approach to the High-Throughput Identification of Honeycomb Materials

Lex M. Rouquette and Alannah M. Hallas

The honeycomb lattice is an iconic structural motif in condensed matter physics. However, emerging theoretical models require the identification of new honeycomb lattice materials with strict specification on their structural, magnetic, and electronic characteristics. In this work, we introduce a filtering algorithm using simple geometric arguments to detect materials with honeycomb structural motifs. We classify four unique categories of lattices: conventional honeycombs, hyperhoneycombs, staircase or zigzag honeycombs, and fully 3D honeycombs. We also identify several distortion motifs in the conventional honeycomb set: elongated, sheared, and buckled honeycombs. We describe several screening criteria for further analysis of honeycomb systems, specifically the quantification of exfoliability in 2D materials, the identification of magnetic honeycombs, and a density-of-states peak quality metric for identification of electronic instabilities. The database containing the results of the filters and subsequent analysis is a useful tool for identifying novel materials for targeted physical phenomena for experimental characterization.
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Strongly Correlated Electrons

Selective coupling of coherent phonons to intertwined charge-orbital and magnetic orders in doped manganites

X. Liu, M. Sander, S.-W. Huang et al. (+15 more)

Strongly correlated materials feature technologically relevant functionalities such as high-temperature superconductivity and colossal magnetoresistance, which emerges from the competition and coexistence of electronic and magnetic phases. Uncovering the microscopic interactions underlying these phenomena remains challenging because spin, orbital, charge, and lattice degrees of freedom are inherently intertwined. Here, by combining time-resolved X-ray diffraction and polarization-resolved ultrafast optical reflectivity in La1/4Pr3/8Ca3/8MnO3, we reveal that coherent phonon modes can selectively track different ordered phases: the in-plane phonon response is predominantly sensitive to charge/orbital order, and the c-axis phonon response is sensitive to magnetic order. Moreover, a ferromagnetic-related hysteresis emerges even when solely probing the charge/orbital-ordered phase, indicating a strong microscopic coupling between the spatially separated charge/orbital-ordered and ferromagnetic-ordered phases. These results demonstrate that coherent phonons provide a direct time-domain route to disentangle intertwined electronic and magnetic dynamics in coupled phases.
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All authors X. Liu, M. Sander, S.-W. Huang, S. Zerdane, A. Caviezel, M. Rössle, J. Lu, D. Babich, S. Shin, E. Pomjakushina, P. Marsik, L. Wang, S. W. Cheong, C. Jia, P. Beaud, H.T. Lemke, U. Staub, R. Mankowsky

Strongly Correlated Electrons · Cross-listed from cond-mat.mes-hall

Real-space Visualization of Emergent Electron Crystals in Rhombohedral Graphene

Yiming Sun, Jinghao Deng, Jiabin Xie et al. (+5 more)

Strongly interacting electrons can spontaneously break spatial symmetries to form electron crystals, exemplified by the Wigner crystal. Recent studies of topological flat bands in rhombohedral graphene have suggested more exotic forms of crystallization, including anomalous Hall crystals that entangle charge order with nontrivial topology and metallic electron crystals in which localized and itinerant carriers coexist. Direct real-space observation of these states, however, has remained elusive. Here we use scanning tunneling microscopy and spectroscopy to visualize emergent electron crystals in rhombohedral hexalayer graphene. At low electric fields and over a finite range of hole doping, we observe electronic lattice patterns that evolve from honeycomb to oblique order through a first-order quantum phase transition with increasing hole density. The Fermi surface extracted from quasiparticle-interference measurements lacks the geometry needed to account for these patterns through conventional nesting. Together with metallic transport and a crystal-site density much lower than the doped carrier density, this supports metallic electron crystals in which a subset of carriers crystallizes. The honeycomb crystal occupies the same phase space as the multiferroic orbital magnetism observed previously in transport and exhibits domain stabilization by a small magnetic field, which may suggest a possible metallic anomalous Hall crystal. With increasing magnetic field, the oblique phase develops a $\sqrt{2}\times\sqrt{2}$ reconstruction with a crystal-sublattice energy splitting that increases linearly with field, corresponding to a $g$-factor of 16. This may reflect an orbital-antiferromagnetic electron crystal with alternating orbital magnetization across the lattice. These results establish a new paradigm of electron crystallization in which charge order is intertwined with orbital magnetism.
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All authors Yiming Sun, Jinghao Deng, Jiabin Xie, Donghan Ge, Hongyuan Li, Takashi Taniguchi, Kenji Watanabe, Xiaomeng Liu

Strongly Correlated Electrons

Remarks on invertible phases with non-onsite symmetry

Ryohei Kobayashi, Kansei Inamura and Ken Shiozaki

We study invertible phases protected by non-onsite symmetries carrying nontrivial lattice anomaly indices. While lattice anomalies are usually viewed as obstructions to symmetric short-range-entangled (SRE) states, we show that anomalous lattice symmetries can nevertheless admit invertible phases that are not SRE, and can moreover shift the set of symmetry-compatible invertible phases. In particular, we consider a fermionic $\mathbb Z_4^F$ symmetry in (2+1) dimensions. For an onsite $\mathbb Z_4^F$ symmetry, symmetric invertible phases have integer chiral central charge $c_-\in\mathbb Z$, whereas a non-onsite symmetry with nontrivial lattice anomaly index obstructs all such phases despite having trivial continuum 't Hooft anomaly. We resolve this by constructing an exact exponentially quasi-local $\mathbb Z_4^F$ symmetry of a $p+ip$ superconductor with $c_-=1/2$. We compute its lattice anomaly, and find that the symmetry indeed forbids $c_-\in \mathbb{Z}$ invertible states. The allowed invertible phases are consequently shifted to $c_-\in\mathbb Z+1/2$. By gauging the fermion parity of the $p+ip$ superconductor, one obtains an Ising topological order enriched by a $\mathbb Z_4$ symmetry. We describe the corresponding symmetry structure in terms of a fusion 2-category. We further show that the $p+ip$ state admits an enlarged non-onsite $U(1)^f$ symmetry, providing an analogue of fractional quantum Hall response in an invertible phase. This non-onsite $U(1)^f$ symmetry again forbids Chern insulators carrying $c_-\in\mathbb{Z}$, while being compatible with invertible states with $c_-\in\mathbb{Z}+1/2$. This result motivates a systematic study of new classes of invertible phases and spin liquids enriched by non-onsite symmetries.
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Strongly Correlated Electrons

Effective Ionic Valence and Local Magnetic Moment in Kagome Superconductors

Ruoshi Jiang, Zi-Jian Lang, Yuzki Oey et al. (+11 more)

In order to understand the unexpected similarity and the correlated behavior in kagome superconductor families AV$_3$Sb$_5$ (A = K, Rb, Cs) and ATi$_3$Bi$_5$ (A = Rb, Cs), we investigate the Hartree-scale local electronic structure of these systems. Our result indicates that V and Ti ions are both of 2+ valence such that the corresponding itinerant carrier densities are similar, and the difference in electron count is instead reflected in their quantum fluctuating ionic magnetic moments. However, due to the frustrated lattice geometry of these materials, such local moments are difficult to experimentally observe via standard probes. For verification, we systematically introduce nonmagnetic Sn impurities to locally relieve the geometric frustration and experimentally demonstrate the existence of well-defined local magnetic moments via magnetic susceptibility and muon spin rotation or relaxation ($\mu$SR) measurements. All experiments discover a systematic increase of magnetic susceptibility upon increasing nonmagnetic impurity level. Our discovered ionic moments suggest a paradigm shift from the existing itinerant carrier-only picture to one incorporating strong correlation from local ionic spins. The associated interatomic and local-itinerant correlations offer a solid ground for the emergence of the observed rich correlated behavior in this new family of superconducting materials.
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All authors Ruoshi Jiang, Zi-Jian Lang, Yuzki Oey, Andrea Capa Salinas, Stephen D. Wilson, Yongwei Li, Ilya Shipulin, Yiwen Zhang, Deng Hu, Zhiwei Wang, Hans-Henning Klauss, Zurab Guguchia, Vadim Grinenko, Wei Ku

Strongly Correlated Electrons

Low temperature thermodynamics of $S_{\mathrm{eff}}=1/2$ triangular lattice quantum spin liquid candidate TlYbS$_2$

Bishnu P. Belbase, Arjun Unnikrishnan, Piyush Chhallare et al. (+8 more)

Geometrically frustrated triangular-lattice antiferromagnets exhibit a delicate competition between magnetic order and quantum spin liquid (QSL) behavior, with the Yb-based delafossite family $A$Yb$X_2$ providing a structurally clean platform for exploring this physics. Here, we report a comprehensive study of single-crystal TlYbS$_2$ using DC magnetization, AC susceptibility, electron spin resonance (ESR), and specific heat measurements extending from room temperature to the millikelvin regime. Single-crystal X-ray diffraction confirms a trigonal $R\bar{3}m$ structure comprising well-separated triangular layers of Yb$^{3+}$ ions with no detectable site disorder. At zero field, a weak thermodynamic anomaly is observed near $530$ mK, which may indicate the onset of a weakly ordered state similar to that reported in KYbSe$_2$. Below $300$ mK, the zero-field magnetic specific heat follows $C_{\rm m}\propto T^{1.8}$, close to a quadratic temperature dependence, in contrast to the linear temperature dependence reported for the sister compound TlYbSe$_2$, which has been described in terms of the interplay between spinons and thermally excited gauge-flux excitations. Magnetization and ESR measurements establish pronounced easy-plane magnetic anisotropy, with $g_\perp/g_\parallel \approx 6.9$. The anomaly near $530$ mK exhibits a strongly anisotropic response to magnetic field. For $H\perp c$, it remains visible up to approximately $2$ T and continuously evolves toward a field-induced ordered phase above approximately $2.5$ T, followed by a sequence of field-induced phases that includes a $1/3$ magnetization plateau between approximately $5$ and $8$ T and full polarization near $17$ T. In contrast, for $H\parallel c$, the anomaly weakens and is suppressed near $3$ T, consistent with the recently reported confinement–deconfinement transition from an ordered state to a field-induced QSL.
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All authors Bishnu P. Belbase, Arjun Unnikrishnan, Piyush Chhallare, Mohan B. Neupane, Eun Sang Choi, Sebastian Erdmann, Muhammad U. Akbar, Mamoun Hemmida, H.-A. Krug von Nidda, Philipp Gegenwart, Arnab Banerjee

Strongly Correlated Electrons · Cross-listed from cond-mat.mtrl-sci

High-Temperature ferromagnetism from site-selective filling in (Fe,Ni)$_{6-\delta}$GeTe$_2$

Tyler L. Werner, Jonathan T. Reichanadter, Xiang Chen et al. (+23 more)

The discovery of high-temperature ferromagnetism in the metallic van der Waals (vdW) system Fe$_N$GeTe$_2$ has brought two-dimensional (2D) magnets into technologically relevant temperature scales. Specifically at N = 5, dilution of magnetic moments by nickel substitution counterintuitively achieves a record high Curie temperature of 478~K. Unraveling the origin of this nickel-substitution-induced enhancement is complicated by the compound's structural complexity, coexistent itinerant and local magnetic contributions, and mesoscopic compositional domains. Through coordinated structural and electronic characterization, we identify that the high-T$_C$ magnetic phase arises from a strain-stabilized Fe$_6$GeTe$_2$ nano-precipitate. Combining first-principles calculations and spin- and angle-resolved photoemission spectroscopy (ARPES), we uncover a site-specific electronic landscape in which interior iron atoms primarily host localized moments while the outer iron atoms neighboring the tellurium layers produce spin-polarized itinerant carriers that cross the vdW gap. The large energy cost associated with homogeneous nickel substitution is found to favor the spontaneous precipitation of the crystallographically and electronically “clean” high-T$_C$ phase. Finally, we compare metal-rich vdW magnets with binary magnetic alloys, and discuss the unifying roles of nano-precipitates in stabilizing otherwise unattainable bulk phases. Our work provides mechanistic insights into the record-high T$_C$ ferromagnetism in (Fe,Ni)$_{5+\delta}$GeTe$_2$, establishing a rigorous foundation for the atomic engineering of vdW magnetic metals informed by direct electronic signatures.
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All authors Tyler L. Werner, Jonathan T. Reichanadter, Xiang Chen, Pranab K. Nag, Luna Y. Liu, Yu-Tsun Shao, Hongrui Zhang, Mingyang Guo, Wenxin Li, Zhibo Kang, Han Wu, Makoto Hashimoto, Donghui Lu, Turgut Yilmaz, Elio Vescovo, Sung-Kwan Mo, Barat Achinuq, Alexei Fedorov, Jacob C. Ruff, Ming Yi, Qiong Ma, David A. Muller, Eduardo H. da Silva Neto, Robert J. Birgeneau, Jeffrey B. Neaton, Yu He

Strongly Correlated Electrons

Sub-cycle doublon-holon dynamics in one-dimensional Mott insulators revealed by two-color high-harmonic spectroscopy

Lance Hatch, Aditya Verma, Eric Schultz et al. (+7 more)

Solid-state high-harmonic spectroscopy is becoming an emerging tool for probing nonequilibrium many-body dynamics. Yet, direct measurements of strongly driven, sub-optical-cycle dynamics in correlated materials during high-harmonic emission remain largely unexplored. Here, we measure high-harmonic emission chirp in a prototypical one-dimensional Mott insulator, which encodes strongly driven doublon-holon dynamics at sub-optical-cycle timescales. We observe a positive chirp for above band gap harmonics, indicating that high harmonics are dominated by doublon-holon recombinations. We further show a harmonic order-dependent dephasing, which can be understood through different doublon-holon excursion distances associated with each harmonic. These results reveal coherent doublon-holon dynamics and their ultrafast dephasing in Mott insulators, which is relevant to other nonequilibrium light-induced phenomena, such as Floquet engineering.
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All authors Lance Hatch, Aditya Verma, Eric Schultz, Hanjun Yang, Priscila Rosa, Genda Gu, Igor Zaliznyak, Giulio Vampa, Laimei Nie, Hanzhe Liu

Strongly Correlated Electrons · Cross-listed from cond-mat.mtrl-sci

Piezomagnetism in a model cubic noncollinear altermagnet

Sudarshan Sharma, Luca Buiarelli, Richard Spieker et al. (+4 more)

Altermagnets constitute a distinct class of magnetic materials that combine compensated magnetic order with spin-polarized electronic bands, hence carrying characteristics of both antiferromagnets and ferromagnets. Piezomagnetism - the linear relationship between lattice strain and a net magnetic moment - has emerged as smoking-gun evidence of altermagnetism that distinguishes it from antiferromagnetism. Here, we uncover a large piezomagnetic response in MnTe2, a cubic altermagnet with a noncollinear spin arrangement and weak spin-orbit coupling. We combine dilatometry with nuclear magnetic resonance, a bulk local probe, to observe signatures of both direct and inverse piezomagnetism consistent with symmetry considerations and first-principles calculations. The dilatometry measurements reveal a shear deformation proportional to an applied magnetic field, while magnetic resonance detects a ferromagnetic moment induced by shear strain. The respective results for the piezomagnetic coupling strength are in good agreement, and they are captured by first-principles results. These findings for simple binary MnTe2 position this material as a model altermagnet, demonstrate the utility of nuclear magnetic resonance in investigations of piezomagnetism, and open new avenues for multimodal strain and magnetic-field control in spintronic and memory applications.
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All authors Sudarshan Sharma, Luca Buiarelli, Richard Spieker, Ivan Jakovac, Damjan Pelc, Turan Birol, Martin Greven

Strongly Correlated Electrons

Block entropy area based non-local fermionic mode optimization with gradient disentanglers

Miklós Antal Werner, Gero Friesecke, Andor Menczer et al. (+2 more)

We introduce a systematic block entropy area based mode optimization algorithm for many-body quantum states of interacting fermions represented by matrix product states. From the gradient of a global cost function, the block entropy area, a long-ranged, non-interacting effective disentangler Hamiltonian is formed. We then simulate the time-dependent Schrödinger equation driven by the disentangler Hamiltonian by employing the time-dependent variational principle based on projector splitting, and minimize the cost function. The combination of the density matrix renormalization group with this gradient-based entanglement minimization forms an efficient low-rank iterative ground-state algorithm that also provides an optimized single-particle basis for matrix product state representation. We demonstrate the method on two-dimensional lattice models of interacting fermions and the Fe${_4}$S${_4}$ cluster, and show its robustness and superiority over earlier protocols using nearest-neighbor mode rotations and reorderings.
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All authors Miklós Antal Werner, Gero Friesecke, Andor Menczer, Kornél Kapás, Örs Legeza

Strongly Correlated Electrons · Cross-listed from cond-mat.mes-hall

Interacting Tomonaga-Lüttinger liquid with impurity for interaction constant $K = 1/2$: Thermopower investigation, entropy variation and heat capacity densities associated with thermoelectric particle transport

Abdellah Touati, Redoune Zamoum and Farhi Houssam Eddine

We investigate thermoelectric and thermodynamic properties of a Tomonaga-Luttinger liquid with interaction parameter $K=1/2$ in the presence of a localized impurity. Using bosonization and refermionization, we derive an exact expression for the thermopower in the nonlinear regime and obtain the corresponding Seebeck coefficient in linear response. At low temperature, the Seebeck coefficient follows a Mott-like relation governed by the energy dependence of the transmission coefficient and is found to be closely related to the entropy per particle. This connection allows us to derive using Kelvin formula the thermopower contribution to the entropy density variation and the charge-carriers contribution to the heat capacity density. Both quantities exhibit Mott-like behavior in the low-temperature regime. We apply our results to a fractional quantum Hall quantum point contact and to a one-channel quantum conductor coupled to an Ohmic environment. Our results demonstrate the close connection between thermoelectric transport and thermodynamic properties in interacting one-dimensional quantum systems.
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Strongly Correlated Electrons

Learning Quantum Matter through Attention in Complex Space

Mingrui Jing, Erdong Huang, Jizhe Lai et al. (+3 more)

Magnetic many-electron wavefunctions require amplitude and phase to be optimized together. Whether a complex internal representation improves this variational search is a practical question for neural wavefunction design. We introduce Complex Psiformer for interacting electrons in a magnetic moiré continuum, combining complex hidden features and Hermitian-magnitude attention with magnetic boundary conditions and fermionic antisymmetry. After the same number of optimization steps, Complex Psiformer reaches lower energies than Real Psiformer in two finite supercells. Both Psiformers also improve on their respective neural Hartree-Fock references. Across five training seeds in the 25-cell system, the mean Complex advantage is 1.458 meV per electron, with a smaller observed spread. A separately trained two-electron Complex state has a smaller energy gap to a finite configuration interaction reference than its Real counterpart. In the Complex states, flux scans show nonmonotonic density correlations and weaker honeycomb mean-density modulation at higher flux, while connected fluctuations persist. Gauge invariant current maps provide a qualitative comparison of local circulation in the optimized states. These benchmarks support the combined architecture as a variational ansatz for studying energies and charge arrangements in finite magnetic systems.
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All authors Mingrui Jing, Erdong Huang, Jizhe Lai, Enji Xiong, Jin-Guo Liu, Xin Wang

Strongly Correlated Electrons

Unraveling the Kagome Antiferromagnetic $3J$ Model and Its Materials: An Integrated Approach

Xin Lu, Andreas Raikos, Menghan Song et al. (+6 more)

We investigate the ground-state and finite-temperature properties of the kagome antiferromagnetic Heisenberg model with three inequivalent couplings, dubbed the $3J$ model, which is designed for the candidate Dirac quantum spin liquid (QSL) material YCu$_3$(OH)$_6$Br$_2$[Br$_{1-x}$(OH)$_x$] (see, e.g., Zeng et al., 2024). Employing large-scale density-matrix renormalization group (DMRG) supplemented by neural quantum states (NQS) simulations, we identify an intermediate QSL phase between two magnetically ordered phases. We also find that this QSL is separated from the kagome spin liquid ground state at the isotropic limit. To establish a direct comparison with experiments, we compute the specific heat of the model by means of advanced exponential (XTRG) and tangent-space (tanTRG) thermal tensor-network methods. In the magnetically ordered phase, the specific heat over temperature exhibits a shoulder at a temperature that is a fraction of the coupling strength $J_{h}$, which disappears in the QSL phase. These universal behaviors are consistent with the experimentally observed specific heat in $3J$ materials for both ordered and QSL candidate samples. Our work thus connects microscopic models with experimentally measurable signatures, exemplifying an integrated approach to understanding QSL phenomena in frustrated quantum magnets~ (see Meng et al., 2026), with $3J$ materials serving as a representative case and providing a foundation for future studies.
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All authors Xin Lu, Andreas Raikos, Menghan Song, Zezong Li, Lankun Han, Shiliang Li, Sylvain Capponi, Zi Yang Meng, Chengkang Zhou

Strongly Correlated Electrons

Acoustic Wave-Function Imaging of Sublattice Physics in a Kagome Lattice

L. Müller, N. Endres, B. Geldiyev et al. (+4 more)

The canonical kagome band structure hosts a Dirac cone, saddle-point van Hove singularities (vHS), and a flat band. Characteristically, these features exhibit distinct sublattice localization within the three-site basis of the kagome lattice. However, experimental proof of this sublattice character is challenging and requires direct access to both the real-space wave function and its associated momentum-space texture. Here, we implement an acoustic kagome lattice on the cm scale and measure the full excitation spectrum, thereby imaging the wave function at each lattice site, including both amplitude and phase. This enables investigation of the momentum-dependent sublattice texture across the complete band structure, particularly at the flat band and at the mixed- and pure-sublattice van Hove singularities. Our results are in excellent agreement with minimal tight-binding model calculations and constitutes the first direct experimental observation of the sublattice-resolved band structure in a kagome lattice.
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All authors L. Müller, N. Endres, B. Geldiyev, S. Widmann, K. Burkard, M. Ünzelmann, F. Reinert

Strongly Correlated Electrons

Certified reduced-basis emulation of conformal field theories on the fuzzy sphere

Virgil V. Baran

Fuzzy-sphere regularization gives numerical access to three-dimensional conformal field theories (CFTs), but locating one requires testing for criticality across the parameter space of microscopic couplings. We reduce the search cost by about two orders of magnitude, combining an exact diagonalization based on states having definite total angular momentum with a certified reduced-basis emulator that reconstructs energies, observables and their derivatives continuously across the couplings from a handful of exact solutions per system size. The combination reproduces the published ground-state-energy analysis of the fuzzy-sphere Ising model and the published conformal data of a three-flavor fuzzy-sphere realization of the O(2) Wilson–Fisher CFT, including quantities defined by parameter derivatives. Applied to the O(2) model with no CFT input, the ground-state-energy criterion locates the critical coupling to within half a percent of a density matrix renormalization group value obtained on systems more than twice the size, and maps the critical line of the model across the coupling plane. Ground-state criteria locate the critical line robustly, but the point they select along it is weakly determined, and the computed dimensions come closest to the bootstrap elsewhere along the line.
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