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Physics Condensed Matter Strongly Correlated Electrons

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Monday 28 September

Strongly Correlated Electrons

Perfect Born Sampling of Symmetric Thermal Tensor Network for Quantum Lattice Models

Jianxin Gao, Qiaoyi Li, Yuan Gao et al. (+5 more)

Accurate calculations of quantum lattice models at low temperatures constitute a major challenge in many-body physics. Stochastic sampling of tensor-network states offers a promising route to tackle this problem; however, existing schemes have long faced a fundamental dilemma—sampling efficiency and symmetry acceleration cannot be achieved simultaneously. Here we propose a perfect Born sampling approach for thermal tensor networks, which performs importance sampling directly from the purified density matrix via the Born rule and incorporates Abelian and non-Abelian symmetries by sampling symmetry quantum numbers. We benchmark the method, realized as both stochastic matrix product states (stoMPS) and stochastic projected entangled pair states (stoPEPS), on large-scale quantum lattice models. Using stoMPS, we accurately simulate the square-lattice Hubbard model on cylinders up to width $W=10$, and study the triangular-lattice Hubbard model down to $T/t = 1/64$, revealing scalar chiral order at half filling and kinetic ferromagnetism upon electron doping. We further extend the stoMPS method to compute finite-temperature quantum dynamics, as demonstrated by the optical conductivity of the Hubbard model, and generalize it to stoPEPS, as showcased on the $20\times20$ square-lattice quantum Ising model at its quantum critical point. Our method combines high sampling efficiency with full symmetry acceleration, and can be used as a state-of-the-art framework for studying both equilibrium and dynamical properties down to ultralow temperatures.
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All authors Jianxin Gao, Qiaoyi Li, Yuan Gao, Chuanshu Xu, Guoliang Wu, Su Yi, Bin-Bin Chen, Wei Li

Strongly Correlated Electrons

Chiral Weyl–Kondo semimetal and circular photogalvanic effect in a prototype Kondo lattice system

Yuan Fang, Kuan-Sen Lin, Mounica Mahankali et al. (+5 more)

Chiral Weyl–Kondo semimetals (cWKSM) provide a setting in which chiral Weyl quasiparticles emerge in the immediate vicinity of the Fermi energy from a Kondo-driven reconstruction of the strongly correlated electronic states in chiral heavy fermion systems (K.-S. Lin et al., arXiv:2602.22185). A defining characteristic of this strongly correlated topological state is the Kramers chiral Weyl fermions in the low-energy quasiparticle states. Recently, experiments in CeGaGe have emerged as a concrete realization of the proposed effect (Arushi et al., preprint). Motivated by these findings, here we go beyond the materials-specific effects by constructing a prototype Kondo lattice model; it incorporates only the essential couplings that respect the associated tetragonal crystalline symmetries. This simplification allows us to robustly demonstrate the symmetry-enforced Kramers Weyl fermions and related topological nodal states in the spectrum of heavy quasiparticles. Furthermore, the simplification provides a tractable setting to determine the salient features in the system's nonlinear optical response, the circular photogalvanic effect, in chiral Weyl–Kondo semimetals. Both analytical and numerical calculations identify sharp peaks in the frequency domain as signatures of the Kondo-driven chiral Weyl nodes; the sharpness of the spectrum reflects the resonant nature of the underlying strongly correlated electronic excitations. Thus, cWKSM provides a unique setting to spectroscopically identify topological fermions that are induced by strong electron correlations. As such, our results are expected to bring about much needed new insights into the understanding of strongly correlated gapless topological matter.
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All authors Yuan Fang, Kuan-Sen Lin, Mounica Mahankali, Arushi, Kevin Allen, Sanu Mishra, Emilia Morosan, Qimiao Si

Strongly Correlated Electrons

t-J model at 50

Józef Spałek

I briefly overview the original formulation of the t-J model starting from Hubbard model, as well as stress its unique features, i.e., advantages and shortcomings when discussing its physical properties. Particular emphasis is put on a brief characterization of connection between magnetism, unconventional superconductivity, and the Mott-Hubbard localization of the correlated carriers in a narrow band. In the second part I summarize the model generalization to the three–orbital situation. The main purpose is to list some basic features of the physics associated with t–J model.
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Strongly Correlated Electrons · Cross-listed from cond-mat.supr-con

Unconventional superconductivity in locally non-centrosymmetric CeNi$_2$As$_2$

Félix Morineau, Jan Knapp, Javier Landaeta et al. (+12 more)

Recent years have seen intense research on heavy fermion superconductivity, inspired by the discovery of multiple superconducting phases in UTe$_\text{2}$ and CeRh$_\text{2}$As$_\text{2}$. In the latter material, two superconducting phases observed under applied magnetic field oriented along the crystallographic $\textit{c}$ direction are associated with local inversion symmetry breaking. To advance understanding of these phenomena, it is highly desirable to find further examples of heavy fermion superconductivity in materials with locally non-centrosymmetric structure. We have succeeded in this quest, by growing single crystals of the CaBe$_\text{2}$Ge$_\text{2}$ isomorph of CeNi$_\text{2}$As$_\text{2}$. The resulting superconductivity brings more than we had foreseen. In addition to providing the opportunity to compare and contrast with that of CeRh$_\text{2}$As$_\text{2}$, the condensation occurs from an incoherent normal state quantitatively similar to that of UBe$_\text{13}$. Our findings therefore raise profound questions not just about superconductivity in the locally non-centrosymmetric structures, but about unconventional superconductivity itself.
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All authors Félix Morineau, Jan Knapp, Javier Landaeta, Thomas Lühmann, Lea Richter, Petra Knappova, Soumen Ash, Sushma Lakshmi Ravi Sankar, Konstantin Semeniuk, Elena Hassinger, Christoph Geibel, Manuel Brando, Daniel F. Agterberg, Andrew P. Mackenzie, Seunghyun Khim

Strongly Correlated Electrons · Cross-listed from cond-mat.quant-gas

A projection operator approach for ultracold bosons coupled to a cavity

Sarbarish Sen, Bimalendu Deb and K. Sengupta

We employ a projection operator technique to study the equilibrium phases and the non-equilibrium quench and ramp dynamics of ultracold bosons described by a two-dimensional (2D) Bose-Hubbard model coupled to a high-finesse cavity with competing local short-range and cavity-mediated long-range interactions. Our analysis relies on a systematic elimination of high-energy virtual hopping processes; this enables us to capture the effects of short-range quantum fluctuations on the phase diagram of the model while treating the cavity-induced long-range interaction within mean-field theory. We find that the phase boundaries between the superfluid (SF), supersolid (SS), charge-density-wave (CDW) and Mott insulating (MI) phases are significantly modified by the presence of these fluctuations. We use this approach to study the dynamics of bosons following a quench/ramp from the CDW to the SS and SF phases; our analysis indicates the presence of oscillatory dynamics characterized by a single frequency due to a quench which takes the system near the critical point. In contrast, for a quench deep inside the SF phase, the dynamics involves multiple frequencies. An explicit comparison with Gutzwiller mean-field theory shows the importance of quantum fluctuations in shaping such post-quench dynamics; this feature may be tested experimentally as we discuss. We also study the ramp dynamics of these bosons and identify a bound on the ramp rate above which the present method is expected to produce accurate results.
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Strongly Correlated Electrons

Quantum-Geometric Amplification of Nonperturbative Interaction Scales

Stefano Bilamour, René Meyer, Johanna Erdmenger et al. (+1 more)

Weak interactions at a two-dimensional quadratic band touching (QBT) can generate an exponentially small symmetry-breaking gap, $m\sim e^{-A/V_1}$, that cannot be captured by every finite order of perturbation theory. We show that the singular quantum geometry of the gapped QBT converts this beyond-all-orders scale into an algebraically enhanced response. The quantum metric develops a momentum-space hot spot whose Brillouin-zone integral diverges logarithmically, and therefore grows algebraically when the gap is dynamically generated by interactions. Through the inverse-frequency Souza–Wilkens–Martin optical sum rule, the same amplification appears in the negative-first longitudinal optical moment, even though the ordinary optical conductivity remains $O(e^2/\hbar)$ and its absorption threshold is exponentially small. We establish these results analytically for a massive QBT and verify them microscopically in an interacting kagome lattice model known to develop a spontaneous quantum anomalous Hall mass at its QBT from loop currents order. Our results identify quantum geometry as an asymptotic amplifier of nonperturbative interaction scales.
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All authors Stefano Bilamour, René Meyer, Johanna Erdmenger, Domenico Di Sante

Strongly Correlated Electrons

Enhanced sliding in the coexisting Charge Density Wave phase of strained TbTe3

Antoine Gallo Frantz, Aleksander Sinchenko, Luc Ortega et al. (+5 more)

In the last years, the application of mechanical tensile stress has been shown to trigger unconventional phases in quantum materials. Recently, an orientational transition of the charge density wave (CDW) of TbTe3 was reported under the application of moderate uniaxial tensile stress, associated to the in-plane a/c lattice anisotropy. This leads to the disappearance of the pristine c-oriented CDW (CDWc) and to the appearance of the orthogonal a-oriented one (CDWa). A coexistence phase with a superposition of CDWa and CDWc appears when a=c. Here, we probe the sliding dynamics of both CDWc and CDWa as a function of applied tensile stress, i.e. in the pure CDWc, pure CDWa and coexistence phases, by measuring current-voltage characteristics and associated differential resistances. If the pristine CDWc has been known to display non-linear dynamics and thus sliding for several years, we show here that the strain-induced CDWa phase also displays the same characteristics, proving its incommensurate nature. Moreover, we show that sliding also takes place both for CDWc and CDWa, with reduced threshold currents, in the coexistence phase, which questions the microstructure of these coexisting orthogonal CDWs in real space. Finally, the linearity of the threshold fields is kept for all deformation states, with finite threshold fields at Tc, which is discussed in terms of commensurability and pinning potentials. This work opens new questions for the theoretical description of sliding CDWs in quasi-2D systems.
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All authors Antoine Gallo Frantz, Aleksander Sinchenko, Luc Ortega, Abdellali Hadj Azzem, Jose Emilio Lorenzo, Pierre Monceau, David Le Bolloch, Vincent Jacques

Strongly Correlated Electrons · Cross-listed from hep-th

Cylinder Defect Casimir Energy and Weyl Anomalies

Yang Zhou

We distinguish two Casimir observables associated with a conformal surface defect. A circular cylinder embedded in flat space has a logarithmic contribution to its Casimir energy, $-d_1\log(R/\epsilon)/(24R)$, fixed by the displacement anomaly. A great cylinder obtained by radial quantization of the ambient theory instead has Casimir energy $-b/(12R)$ in the conformal defect vacuum with a fixed local anomaly convention. Free-field and holographic calculations provide checks of the proposed relations in both embeddings.
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Strongly Correlated Electrons

Electronic and topological properties of Ce-based honeycomb ferromagnet Ce$_2$Zn$_6$Ge$_3$

Yanen Huang, Zihan Yang, Jiawen Zhang et al. (+7 more)

Ce$_2$Zn$_6$Ge$_3$ is a rare example of the Ce-based honeycomb ferromagnet. Here, we report its Fermi surface and topological properties by quantum oscillations via the magnetoresistance and tunnel diode oscillator (TDO) based measurements, in combination with the density functional theory (DFT) calculations. Four fundamental frequencies are observed in the quantum oscillations, and their angle dependence is more compatible with the DFT calculations assuming that the 4$f$-electrons are localized, suggesting a localized nature of ferromagnetism in Ce$_2$Zn$_6$Ge$_3$. Furthermore, the observations of negative longitudinal magnetoresistance and non-zero Berry phase, as well as the existence of two pairs of Weyl points near the Fermi level as revealed from the calculated electronic structures, provide strong evidence for nontrivial topology in Ce$_2$Zn$_6$Ge$_3$. These findings suggest that Ce$_2$Zn$_6$Ge$_3$ could provide a unique platform to study magnetism, topology, quantum criticality and their interplay.
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All authors Yanen Huang, Zihan Yang, Jiawen Zhang, Yuwei Zhou, Lubin Wang, Gang Li, Michael Smidman, Chao Cao, Yu Liu, Huiqiu Yuan

Strongly Correlated Electrons · Cross-listed from hep-th

RG Limit Cycles in BKT Flows $\equiv$ Periodic Real-Time Dynamics in the Current-Current Perturbed $SU(2)_1$ WZW Model

Parameshwar R. Pasnoori

We establish an exact correspondence between renormalization-group (RG) evolution and real-time quantum dynamics in the anisotropic current-current perturbed $SU(2)_1$ Wess-Zumino-Witten (WZW) model. Using its integrable fermionic representation, we construct the exact time-dependent many-body wavefunction by means of the generalized Bethe ansatz and show that periodic boundary conditions lead to quantum Knizhnik-Zamolodchikov equations associated with the XXZ trigonometric $R$-matrix, which corresponds to the quantum affine algebra $\mathcal{U}_q(\widehat{\mathfrak{sl}_2})$ evaluated in its spin-$1/2$ evaluation representation. Consistency of these equations constrains the temporal evolution of the longitudinal and transverse interaction strengths. In the universal regime, these integrability conditions are exactly equivalent to the Berezinskii-Kosterlitz-Thouless RG flow equations upon identifying physical time with the logarithmic RG scale. Consequently, the RG limit cycles of the anisotropic current-current perturbed $SU(2)_1$ WZW model are realized as periodic real-time evolution of its interaction strengths. Our results provide an exact dynamical realization of RG limit cycles and establish a direct connection between cyclic RG flows, quantum integrability, and periodically driven interacting quantum field theories.
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Strongly Correlated Electrons

Bogoliubov coupled-cluster theory for su(2) Hamiltonians

Swarnamoy Ghosh, Thomas M. Henderson and Gustavo E. Scuseria

Coupled-cluster theory is the method of choice for weakly correlated systems, but in strongly correlated systems where the mean-field reference is qualitatively poor, it can break down badly. These failures can be ameliorated by using symmetry-broken mean-field references. For systems that spontaneously break spin symmetry, we might favor an unrestricted reference. In systems that instead break number symmetry, we turn to Bogoliubov coupled cluster theory. In this work, we apply Bogoliubov coupled-cluster to Hamiltonians with an underlying su(2) algebra to study the pairing Hamiltonian and the spin XXZ and J1-J2 models by exploiting the correspondence between fermionic-pair operators and spin-1/2 operators. For the pairing problem, the reference is the usual Bardeen–Cooper–Schrieffer (BCS) quasiparticle vacuum, while for spin systems we use the analogous spin-BCS reference, which breaks Sz symmetry and provides a flexible starting point for strongly correlated regimes. Correlation is incorporated through a hierarchy of coupled-cluster approximations. Beyond energies, we compute the response density matrices for the evaluation of spin–spin correlation functions for the XXZ and J1-J2 Heisenberg models, and the pairing parameter and particle-number variance for the pairing Hamiltonian. We also derive the corresponding relaxed density matrices, including the effects of orbital relaxation. Benchmark calculations for the half-filled pairing Hamiltonian and spin models demonstrate that Bogoliubov coupled cluster provides a systematically improvable wave-function-based approach for su(2) Hamiltonians, including geometrically frustrated spin systems requiring complex and noncollinear BCS references.
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Strongly Correlated Electrons · Cross-listed from math-ph

The equivalence of topological indices for $\mathrm{U}(1)\rtimes\mathbb{Z}_2$-symmetric quantum spin chains

Hal Tasaki

Symmetry-protected topological (SPT) phases in quantum spin chains are distinguished by topological indices. Ogata's operator-algebraic indices apply to a broad range of symmetry classes without requiring continuous symmetry, whereas the elementary twist index of Tasaki requires $\mathrm{U}(1)$ symmetry. We prove their equivalence in the common setting of integer-spin chains with on-site $\mathrm{U}(1)\rtimes\mathbb{Z}_2$ symmetry and a symmetric locally-unique gapped ground state, without assuming translation invariance or a matrix product representation. A charge-fluctuation estimate yields a strong-limit construction of half-chain rotations with their phases fixed. An exact group commutator identity then identifies the Ogata index with the limit of local twist expectations and gives an explicit error bound. This provides a computable formula for the index when a lower bound on the gap and the relevant ground-state expectations are available. Combining the equivalence with a recent boundary-field gap theorem of OpenAI and our earlier twist-index calculation, we obtain a spin-rotation-invariant locally-unique gapped ground state of the infinite $S=1$ antiferromagnetic Heisenberg chain with both indices equal to $-1$, without assuming infinite-volume uniqueness. The author formulated the problem and proposed the basic strategy, while ChatGPT Astra made substantial contributions to the development of the proof.
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Sunday 27 September

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

Superconducting Pairing Symmetry on Geometric-Algebra Foundations via the Scalar-Projection Method

Youping Dai

We formulate the low-energy theory of superconducting pairing in the geometric algebra $Cl_{3,0}$. Conventional BCS mean-field theory and its extensions ($s$-, $p$-, $d$-wave, etc.) have algebraic counterparts in an eight-dimensional real multivector space. The construction is a two-level projection: matrix blocks are represented as Clifford multivectors, and their grade-0 projected geometric products extract the scalar blocks from which Hamiltonians are built. The result is an algebraic reconstruction, physically equivalent to the standard complex-matrix formulation. In this reconstruction, the dichotomy of pairing channels acquires an algebraic root: it follows from the fermionic identity $B^\dagger(V)=-B^\dagger(V^{\mathsf T})$, and the Fierz rearrangement is realized by the map $\Phi:G\mapsto Ge_{31}$ (with $e_{31}^2=-1$). This yields a kernel/matrix dictionary: at the effective-kernel level grades $0\oplus3$ correspond to spin singlets and grades $1\oplus2$ to triplets; at the pairing-matrix level the singlet plane is $\mathrm{span}\{e_2,e_{31}\}$. The BCS limit has a double grade identity: kernel grade 0 (scalar glue) and vertex grade 2, a bivector ($i\sigma_2\leftrightarrow e_{31}$). We state three algebraic results: (i) a decomposition theorem for BdG quantum geometry with a null-texture criterion, applied to the chiral-state controversy in CsV$_3$Sb$_5$; (ii) a Fierz sign duality in the four-dimensional Minkowski algebra, with a chirality-reversal extension to two-node Weyl-semimetal models; (iii) an error bound and condition-number structure for tomographic reconstruction under a linear-response probe model. Illustrations include a glue-generation mechanism, a one-loop algebraic renormalization flow whose feeding constant coincides in magnitude with the $\mathfrak{su}(2)$ Casimir, closed-form $\mu=0$ inter-node spectra, and a UTe$_2$ two-phase analysis.
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Strongly Correlated Electrons · Cross-listed from quant-ph

Autonomous phase discovery

Shiyu Zhou, Yuxuan Zhang, Sebastian Wetzel et al. (+2 more)

Understanding quantum phases of matter has long relied on physicists' intuition and mathematical tools such as symmetry and topology. Remarkably successful as these approaches have been, they provide no universal way to explore a Hamiltonian space whose organizing principle is not known in advance. In this work, we introduce a fully autonomous system combining differentiable programming and unsupervised learning for quantum phase discovery. The search evaluates ground-state data along an adaptive trajectory rather than on a predetermined parameter grid. We demonstrate the system with three different solvers and benchmark it against random sampling at equal ground-state-evaluation budgets. On a generalized cluster chain hosting up to $200$ distinct phases, the search finds up to $25$ more phases at the same budget, and matches random sampling given thirty times its budget. On a $50$-parameter Chern insulator, it reaches sectors not obtained by the simple harmonic constructions considered here, in a family whose inverse problem remains open, while recovering all sectors found by sampling. Our results establish autonomous, gradient-driven exploration of Hamiltonian space as a practical route to discovering quantum phases without phase labels or a prescribed target phase.
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All authors Shiyu Zhou, Yuxuan Zhang, Sebastian Wetzel, Roger Melko, Xiu-Zhe Luo

Strongly Correlated Electrons

Scaling Theory for Learning Low-Energy Quantum Subspaces

Guijing Duan, Chen Mo and Di Luo

Phase diagrams and energy surfaces require low-energy states across a family of Hamiltonians, but solving each parameter point independently is prohibitively expensive. An important question is not how a single labeled eigenstate behaves under parameter variation, but how much information about the low-energy sector is contained in a small set of reference wavefunctions. We show that the physically relevant object is the isolated low-energy subspace itself: it remains well defined through degeneracies and level crossings, and it can be learned efficiently from nearby sampled states. Working in this subspace, we prove that a sampling pattern cancelling the first $q$ nonconstant response orders yields an energy-density error bounded by $d^{2(q+1)}$ for every retained level, where $d$ is the parameter-space sampling distance. For a gapped local ground state on $n$ sites, locality sharpens this to $d^2(nd^2)^q$, identifying $nd^2$ as the natural scaling variable governing the effectiveness of higher-order information from sampled wavefunctions. In a local analytic regime this gives a sampling cost $K=\mathcal{O}([\log(1/\varepsilon)]^D)$ at fixed parameter dimension $D$. Numerical results on Heisenberg and transverse-field Ising chains confirm the distance scaling law and the $nd^2$ collapse. Beyond characterizing learnability, the scaling behavior further provides a finite-size probe of phase transitions near criticality.
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Strongly Correlated Electrons

Generalized {\eta}-pairing eigenstates in three-component Hubbard models under a transverse field

F. X. Liu and Z. Song

We investigate three-component Hubbard models on a bipartite lattice in the presence of a trans?verse field. Unlike the two-component Hubbard model, where the {\eta}-pairing symmetry survives the transverse field, the three-component model possesses neither {\eta}-pairing symmetry nor conservation of the particle number of each component. We introduce a generalized {\eta}-pairing operator, formed as a hybridization of three types of two-component pairing operators, and employ the restricted spectrum-generating algebra to construct a family of exact eigenstates. These eigenstates exhibit off-diagonal long-range order. Furthermore, we construct an exact tensor-product state whose co?herent periodic dynamics provide an exact realization of quantum many-body scar dynamics while simultaneously exhibiting long-range magnetic order. We also propose three protocols for preparing this state via quench dynamics, and verify their effectiveness through numerical simulations.
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Strongly Correlated Electrons

Kitaev-Heisenberg model on the square-hexagon-dodecagon lattice

Saeed Barari, Yasir Iqbal, Ganapathy Baskaran et al. (+3 more)

We study the spin-$1/2$ Kitaev-Heisenberg model on the square-hexagon-dodecagon lattice with a symmetry-preserving tri-coloring of the Kitaev exchanges. We focus on two cases: (i) the pure Kitaev model with anisotropic exchanges and (ii) the Kitaev-Heisenberg model with isotropic Kitaev exchange. In the absence of Heisenberg interactions, we use the standard mapping of the Kitaev model onto a quadratic Majorana-fermion problem in a $\mathbb{Z}_2$ gauge field. We find a gapped energy spectrum throughout the positive-coupling phase diagram, except at a single point where the twofold-degenerate energy bands form a Dirac cone. This unique gapped region corresponds to a toric code phase. However, depending on the couplings, vortex excitations on square, hexagonal, and dodecagonal plaquettes realize three distinct relative assignments to the $e$ and $m$ anyons. We determine these relative assignments from the physical fermion parity of the vortex sectors and locate their boundaries by tracking zero crossings of vortex-bound Majorana levels. For the isotropic Kitaev-Heisenberg model, we combine graph-based projected entangled-pair-state calculations, exact diagonalizations, and linear spin-wave theory to study the entire phase diagram. Apart from the toric code topological phases that are robust around the Kitaev limits, we obtain four collinear magnetically ordered phases that can be characterized by their local and relative orderings of hexagonal plaquettes. We also identify a special point at which the ground state is a product state.
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All authors Saeed Barari, Yasir Iqbal, Ganapathy Baskaran, Saeed S. Jahromi, Chunxiao Liu, Julien Vidal

Strongly Correlated Electrons · Cross-listed from math.QA

Inequivalent modular tensor categories with identical $S$, $T$ and $W$

Ran Luo and Jiahua Tian

It remains an open question whether the modular data $(S,T)$ together with the Whitehead-link matrix $W$ determine a modular tensor category up to ribbon equivalence. We answer negatively by constructing two braided-inequivalent Dijkgraaf–Witten modular categories for $(\mathbb Z/p\mathbb Z)^3$ for prime $p\ge5$ with identical $(S,T,W)$ and, more generally, identical Reshetikhin–Turaev invariants of all framed oriented links with at most two components under a single bijection of simple objects. The construction varies an alternating $3$-cocycle while fixing a quadratic cohomology class, using restriction to subgroups of rank at most two to match link invariants and the quadratic and alternating classes together to obstruct braided equivalence. A complete classification of modular tensor categories up to ribbon equivalence therefore requires invariants beyond those of colored framed links with at most two components. We also analytically evaluate an uncolored partition function on a closed oriented three-manifold that separates all $(p-1)/2$ equivalence classes in the family.
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Saturday 26 September

Strongly Correlated Electrons

How Much Do We Understand Ce L3 XANES? Ab Initio Insights into Configuration-Specific Screening at the Multiplet–Continuum Frontier

Alessandro Mirone

How can local multiplet signatures, collective core-hole screening, and an extended photoelectron be reconciled in Ce $L_3$ x-ray absorption near-edge spectra? Motivated by the question raised by Kvashnina [Chem. Eur. J. 30, e202400755 (2024)], we address this challenge using XSpectruplet, which couples local multiplet dynamics to continuum photoelectron propagation in self-consistent Kohn–Sham screening potentials. For Ce$^{4+}$ in CeO$_2$, our heuristic search identifies primary and secondary stationary screening states whose calculated white-line maxima lie about 7.3~eV apart after including their independently calculated total-energy difference, yet both retain the same effective local spectroscopic $4f^0$ sector. Their squared overlaps with the unrelaxed sudden reference give approximate statistical weights of 63% and 30%, respectively, within an independent-channel description. Their contrasting screening responses arise from collective rehybridization of occupied orbitals, rather than occupation of an additional localized $4f$ spectator, and produce contributions in both the main white-line and satellite regions. Ce$^{3+}$ in monazite CePO$_4$ provides the contrasting case of a localized $4f^1$ spectator participating explicitly in the multiplet dynamics. Independent relaxation of neutral $4f$ and white-line states gives a CeO$_2$ pre-edge–white-line gap of 10.51~eV, close to the experimental separation of approximately 10.7~eV. Its excess over the fixed-background spectral gap defines a net correction, which we transfer heuristically to CePO$_4$ without changing its local multiplet structure. This gives an estimated CePO$_4$ gap of 6.38~eV, compared with approximately 8.1~eV experimentally. Distinct spectral contributions can thus arise from collective screening without a change in the effective local configuration.
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Strongly Correlated Electrons

GEM: An implementation of the ghost-Gutzwiller approximation for simulating interacting quantum systems

Samuele Giuli, Tsung-Han Lee, Yong-Xin Yao et al. (+6 more)

We present GEM (Ghost Embedding Method), an open-source software package written in Python for computing equilibrium properties of strongly correlated electronic systems within the ghost-Gutzwiller approximation method. GEM provides a computationally efficient framework for studying multi-orbital lattice models. It supports zero- and finite-temperature calculations and symmetry broken phases. It is integrated with the TRIQS ecosystem, providing tools for model construction, self-consistent solution, and evaluation of physical observables. We first detail the method's theoretical formulation, then we present the software architecture, and finally we introduce some practical workflow, which also validates the implementation against established results. In particular, we illustrate the capabilities of GEM through multiorbital and finite-temperature applications and discuss its computational cost relative to more demanding quantum embedding approaches.
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All authors Samuele Giuli, Tsung-Han Lee, Yong-Xin Yao, Ina Park, Harrison LaBollita, Ivan Pasqua, Nils Wentzell, Nicola Lanatà, Olivier Gingras

Strongly Correlated Electrons

Symmetry-permuting entanglers for non-invertible symmetry-protected topological phases

Minyoung You

1+1D symmetry-protected topological (SPT) phases with invertible symmetry can be characterized by the symmetric entanglers: globally symmetric finite-depth local unitary circuits that generate representative ground states from a product state. For non-invertible symmetries, however, distinct SPT phases, such as the three $\mathrm{Rep}(D_8)$ SPT phases, may not be connected by any symmetric entangler. We show that the three $\mathrm{Rep}(D_8)$ SPT phases can nevertheless be connected by symmetry-permuting finite-depth local unitary circuits, realizing dualities predicted by topological quantum field theory (TQFT). We construct an explicit matrix product unitary connecting two of the $\mathrm{Rep}(D_8)$ SPT phases, and show that its action on string order parameters reproduces the anyon permutation predicted by the TQFT duality.
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Friday 25 September

Strongly Correlated Electrons

Chiral Weyl-Kondo semimetallic state through enhanced correlation in CeGaGe

Arushi, Kevin Allen, Yuan Fang et al. (+11 more)

Strongly correlated chiral materials have been proposed to host a chiral Weyl-Kondo semimetal (cWKSM) state, in which Kondo hybridization pins chirality-induced Kramers-Weyl point crossings, together with additional symmetry-enforced band crossings, near the Fermi level. Realizing this state requires a material that combines crystal chirality, non-symmorphic symmetry, and Kondo correlations, and currently there are no known materials that combine all these requirements. Here we report evidence for a cWKSM state in CeGaGe, a member of the RXY (R = rare earth; X = Al, Si; Y = Ga, Ge) family. Magnetization measurements confirm long-range antiferromagnetic order below T$_N$ = 4.7 K with a complex, canted magnetic structure. Unique to CeGaGe among the known RXY systems is a structural transition from an achiral tetragonal I4$_{1}$md structure (at high temperatures) to the chiral tetragonal P4$_{3}$ structure (at low temperatures). The structural transition in CeGaGe allows us to highlight the role of chirality in stabilizing the Kramers cWKSM state. Hall resistivity measurements with $H || c$ reveal an anomalous Hall conductivity (AHC) that is constant below the Kondo temperature $T_K \approx 7$ K and drops sharply above it. This crossover tracks the onset of Kondo coherence rather than the magnetic ordering, which occurs at T$_N$ = 4.7 K. Together with first-principles calculations for the $P4_3$ structure, this identifies the AHC as an intrinsic, Berry-curvature-driven contribution generated by Kondo hybridization, rather than a consequence of extrinsic scattering or dynamic scalar spin chirality. These results establish CeGaGe as a rare experimental platform in which crystal chirality, strong electronic correlations, and non-trivial band topology coexist, providing the first material realization of a Kondo-driven cWKSM state.
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All authors Arushi, Kevin Allen, Yuan Fang, Kuan-Sen Lin, Mounica Mahankali, Hari Bhandari, Karthik Rao, Alberto Ruiz Biestro, Christopher Lane, Jian-Xin Zhu, Sanu Mishra, Geoffroy Hautier, Qimiao Si, Emilia Morosan

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

Quantum Geometric Origin of Yu-Shiba-Rusinov States

Rui-Xing Zhang

In this work, we revisit the classic Yu-Shiba-Rusinov (YSR) problem of magnetic impurities in $s$-wave superconductors and uncover a quantum geometric origin of the YSR bound-state structure. The key geometric quantity is the momentum-space average of Bloch band projector over low-energy electrons, whose matrix rank, positive eigenvalues, and corresponding eigenvectors directly control the number, energies, and symmetry representations of the YSR states, respectively. As a result, a superconductor with nontrivial normal-state quantum geometry can host more bound states than its trivial counterpart, even if they share the same electronic dispersion. We apply our theory to monolayer $1H$-NbSe$_2$ and find that the geometric texture of its single superconducting band enforces three symmetry-distinct YSR channels for a magnetic point impurity at Nb or Se sites. Our work opens a route to probing normal-state wavefunction geometry through local YSR spectroscopy.
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Strongly Correlated Electrons

Read-Rezayi fractional Chern insulators in modulated Bernal graphene

Ruth Mora-Soto, André Grossi Fonseca, Raul Perea-Causin et al. (+3 more)

Fibonacci anyons provide a universal platform for topological quantum computation, and emerge as low-energy excitations in the $\mathbb{Z}_3$ Read-Rezayi phase in the fractional quantum Hall effect. However, realistic microscopic realizations of this phase in the absence of a magnetic field have remained elusive. We study a model of periodically modulated Bernal bilayer graphene with gate-screened Coulomb interactions. Using the recently developed target-phase optimization method in conjunction with band-projected exact diagonalization, we identify at filling $\nu=3/5$ a region of parameter space whose ground state is consistent with a Read-Rezayi fractional Chern insulator. The partially filled band from which it arises is a part of a two-band complex which mimics geometric aspects of the lowest and first Landau levels, with the ground state at $\nu=1/2$ consistent with the Moore-Read state. Our results suggest that modulated Bernal graphene can realize delicate non-Abelian fractional quantum Hall states at zero magnetic field, while demonstrating target-phase optimization as a practical route to discovering such phases in realistic, high-dimensional microscopic models.
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All authors Ruth Mora-Soto, André Grossi Fonseca, Raul Perea-Causin, Hui Liu, Emil J. Bergholtz, Marin Soljačić

Strongly Correlated Electrons

Zoology of chiral superconductors in Chern bands

André Grossi Fonseca, Aidan Reddy, Ahmed Abouelkomsan et al. (+2 more)

Evidence for chiral superconductivity has recently been observed in several van der Waals systems including rhombohedral multilayer graphene and twisted bilayer MoTe$_2$. In the latter, superconductivity emerges at carrier densities near a fractional Chern insulator. This raises the question of what kinds of superconductors may emerge in a system of electrons in a topological band with strong repulsive interactions. Here, we adapt the target-phase optimization method to search for chiral superconductors in a minimal model of interacting electrons in a Chern band. We construct a differentiable loss function for superconductors from the sign oscillation of the pair-binding energy and combine gradient-based optimization with a rigorous screening procedure to identify and characterize superconductors. Applying this framework within exact diagonalization to spinless electrons in periodically modulated Landau levels with screened Coulomb interactions, we uncover a broad family of chiral superconducting phases. At filling $\nu=2/3$, we recover the previously identified $f-\mathrm{i} f$ hole superconductors and find additional $p\pm \mathrm{i} p$ and $f+\mathrm{i} f$ superconductors of both electrons and holes, occurring near and far from the limit of ideal quantum geometry. At $\nu=1/2$, we identify $p- \mathrm{i} p$ electron and $f-\mathrm{i} f$ hole superconductors and find, for the first time, a direct transition between chiral superconductors and composite Fermi liquids. Our results reveal that chiral superconductivity in Chern bands comprises a diverse landscape of competing pairing instabilities and establish target-phase optimization as a general strategy for searching for quantum phases in complex interacting systems.
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All authors André Grossi Fonseca, Aidan Reddy, Ahmed Abouelkomsan, Liang Fu, Marin Soljačić

Strongly Correlated Electrons

Emergent low-energy many-body Hilbert spaces in Chern bands

Chen-Xin Jiang, Zi-Xiang Hu and Bo Yang

We show that in Landau levels and more generic Chern bands, the most relevant many-body subspace selected by realistic two-body interactions alone (e.g., in the limit of vanishing bandwidth and band gap) depends strongly on the particle density and can be constructed systematically. Using the well-defined hierarchical structure of conformal Hilbert spaces (CHS), each with a highest-density vacuum state, we compute, for both fermionic and bosonic systems, the many-body quantum metric that quantifies the interaction energy scales of these subspaces. For a large family of short-range, Coulomb-based interactions, particles preferentially occupy the many-body states in the smallest accommodating CHS. This allows us to describe the low-energy physics of the interacting system in terms of the appropriate anyonic degrees of freedom. Our results also explain why, in any Chern band (in lattice or continuum systems), band mixing tends to be suppressed even in the limit of strong interaction; this suppression is stronger when the band deviates less from the ideal trace condition and when the two-body interaction is shorter-ranged.
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Strongly Correlated Electrons · Cross-listed from quant-ph

Probing the classical complexity of quantum dynamics experiments

Thomas Schuster and Andreas Elben

A confluence of recent works has shown that many quantum circuits and dynamics are efficiently simulable by classical algorithms that track local information, even when conventional complexity measures such as the entanglement and magic are high. Here, we introduce a novel measure of complexity, the reactivity, to capture this new method of classical attack. Unlike conventional complexity measures, the reactivity does not capture a property of a quantum state or operator in isolation, but rather a quantum experiment as a whole. We provide numerical and rigorous evidence that quantum experiments with low reactivity are simple by a host of measures: they are efficient to classically simulate, learn, and fast-forward. This motivates the search for quantum experiments with high reactivity, which may evade these simplistic features. To this end, we introduce easily implementable experimental protocols—dubbed Pauli path spectroscopy—that allow one to efficiently measure the reactivity of any quantum experiment of interest. Our protocols are applicable even when the experiment itself is beyond the reach of classical simulation.
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Strongly Correlated Electrons

Quantum Representation Selects Neutral Skyrmion Molecules

Vishnu Jejjala

Skyrmions experience a sideways gyroscopic force when they move. Bound molecules can cancel this force; we call them gyroscopically neutral. We show that the quantum states available on each site of a magnet select the composition needed for cancellation. In two models of $SU(3)$ magnetism, this composition changes from a pair to a trimer. Both models assign exactly the same energy to every configuration of their common classical order parameter, isolating the effect of the local quantum states. Neutral molecules can also unwind when additional local states are allowed. Mean field calculations nevertheless find both compositions bound and locally stable, with the neutral trimer surviving sampled interaction changes. Comparing their motion reveals the changed cancellation rule, and prepared neutral molecules translate over short distances with little deformation.
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Strongly Correlated Electrons

A Unified Spin-Fermion Framework for Magnetic Diversity in Chromium Monopnictides

Ruoshi Jiang and Bartomeu Monserrat

Isoelectronic compounds are generally expected to exhibit related electronic, structural, and magnetic behavior. Chromium monopnictides CrX (X= Sb, As, P), however, display a striking evolution from high-temperature altermagnetism in NiAs-type CrSb, through double-helical antiferromagnetism in MnP-type CrAs, to the absence of resolved long-range magnetic order in MnP-type CrP. Here, combining first-principles calculations in the non-collinear Curie-paramagnetic state, structural analysis, magnetic phase-diagram calculations, and exchange-parameter extraction, we establish a unified microscopic framework for this evolution. All three compounds share a formal high-spin $d^5$ configuration, nominally Cr$^{1+}$, coupled to itinerant states of predominantly pnictogen character. From Sb to P, chemical pressure enhances ligand itinerancy and drives the structural evolution from the high-symmetry NiAs lattice to increasingly distorted MnP-type networks. The accompanying reconstruction of competing Cr-Cr exchanges favors A-type antiferromagnetism in CrSb and double-helical order in CrAs, while placing CrP near a frustrated regime with closely competing magnetic tendencies. Our results establish chemical-pressure-driven exchange reconstruction as a general mechanism through which a common spin-fermion electronic structure can generate contrasting magnetic phases in strongly correlated materials.
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Strongly Correlated Electrons · Cross-listed from cond-mat.mes-hall

Emergent frustrated magnetism in strain-patterned graphene

Yu-Chiang Hsieh, Wen-Han Kao, Christophe De Beule et al. (+18 more)

Geometrically frustrated magnetism conventionally arises from pre-existing magnetic moments on lattices whose geometry prevents their interactions from being simultaneously satisfied, giving rise to highly degenerate states and rich collective behavior. Creating such frustration in an intrinsically non-magnetic material presents a fundamentally different challenge, requiring both the magnetism and the competing interactions to emerge from correlated electrons. Here we show that this can be realized in graphene through lithographically programmable strain engineering. Patterning strain and the associated pseudo-magnetic field (PMF) into superlattices creates a correlated electronic system with flat bands and strong interactions. Transport measurements reveal interaction-driven insulating behavior, anisotropic magnetic hysteresis, and slow relaxation dynamics reminiscent of spin freezing, qualitatively captured by Monte Carlo simulations of competing magnetic moments on the PMF-defined ruby superlattice. Cryogenic magnetic force microscopy further reveals magnetic textures associated with the PMF landscape. These observations demonstrate frustrated magnetism emerging from correlated electrons in otherwise non-magnetic graphene. Our results establish lithographic strain engineering as a general and scalable route to flat bands and correlated states in van der Waals materials, providing a versatile platform for programmable quantum matter.
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All authors Yu-Chiang Hsieh, Wen-Han Kao, Christophe De Beule, Sheng-Zhu Ho, Ru-Long Gou, Bo-Nian Chen, Kuan-Yu Chou, Kuo-En Chang, Chin-Chia Chang, Ying-Mei Yang, Ching-Hua Kao, Hao-Chien Chiang, Jyun-Lin Chen, Sheng-Chin Ho, Kenji Watanabe, Takashi Taniguchi, Ming-Hao Liu, Ching-Hao Chang, Yi-Chun Chen, Ying-Jer Kao, Tse-Ming Chen