Papers

Janus-particle arrays provide a soft-matter platform in which particle orientations act as classical spins with anisotropic, bond-dependent interactions. Motivated by recent experiments on triangular arrays of metallodielectric Janus particles exhibiting sixfold orientational order and directly observable vortices and antivortices, we study effective models beyond the isotropic XY description. A classical $120^\circ$ compass model captures the minimal bond-directional interaction, while an effective Kern–Frenkel model incorporates the geometry of the Janus surface interaction more directly. Monte Carlo simulations show that both models exhibit a low-temperature sixfold ordered phase, a high-temperature disordered phase, and an intermediate quasi-long-range-ordered regime consistent with two Berezinskii–Kosterlitz–Thouless transitions. In both cases, the sixfold order arises through thermal order-by-disorder from a continuously degenerate ferromagnetic manifold. We further show that higher-order extensions of the $120^\circ$ interaction can alter the orientational selection: a quadratic term reverses the fluctuation-induced sixfold anisotropy, while a cubic term lifts the degeneracy energetically and selects the lattice-aligned directions that coincide with those observed experimentally. These results connect the microscopic anisotropy of Janus-particle interactions to emergent XY-like vortex physics and illustrate how distinct microscopic mechanisms can produce similar sixfold orientational order.

We study the phase diagram of the spin-1/2 XXZ Heisenberg chain in a staggered magnetic field. An exact solution is obtained along the phase boundary, where the exchange anisotropy and the staggered-field strength satisfy an exact analytical relation, yielding a highly degenerate manifold of ground states with off-diagonal long-range order. We demonstrate that these exact ground states lie on the boundary between the ferromagnetic phase and a gapless Luttinger liquid phase. Upon further decreasing the anisotropy, the gapless phase eventually gives way to a gapped quantum-disordered phase. Large-scale density-matrix renormalization group calculations confirm this phase structure and indicate that the transition across the exact boundary is of first order. Our results provide an exact benchmark for understanding quantum phase transitions driven by staggered magnetic fields in one-dimensional quantum spin systems.

Quantum materials are characterized by intertwined orders, and a fundamental goal in condensed matter physics is to achieve their selective control in such a way that one order parameter can be tuned while leaving others largely unaffected. Although significant progress has been made in thermal equilibrium, realizing such control out of equilibrium remains highly challenging. Here we employed in-situ tensile strain to selectively manipulate the photoinduced lattice dynamics associated with ferroelectric and magnetic orders in multiferroic BiFeO$_3$. By applying MeV ultrafast electron diffraction to freestanding BiFeO$_3$ membranes under tunable strain, we showed that tensile strain markedly suppresses the ultrafast photoinduced reduction of the ferroelectric displacement. By contrast, the photoinduced dynamics of the antiferrodistortive rotation of the oxygen octahedra, which modulates the magnetic order, remains insensitive to strain. Not only do these findings reveal distinct microscopic pathways underlying nonequilibrium multiferroic dynamics, they also establish tunable strain as an effective route for engineering ultrafast phase control in correlated materials.

A Devil's staircase is a sequence of transitions between topological sectors as a control parameter is varied. Such staircases are predicted in frustrated magnets and lattice gauge theories, but observing them is hard: the winding number that labels each sector is topologically protected, so local quantum dynamics alone cannot move the system from one step to the next. Here we propose and analyze an experimentally feasible way to realize a thermal quasi-Devil's staircase in a finite Rydberg-atom array. We study the anisotropic triangular-lattice Ising antiferromagnet using a dimer mapping, a directed-string description, exact thermodynamics, and Monte Carlo simulations. In the defect-free string manifold, the commensurate–incommensurate onset follows from a simple energy–entropy balance, and the exact Ising critical relation reduces to the same condition when triangle-rule defects are rare. On a finite lattice, this onset appears as a quasi-Devil's staircase of winding-sector crossovers, which we resolve through winding distributions, structure factors, and directional correlations. The key point is that thermal fluctuations overcome the topological barriers that block sector changes under purely quantum dynamics, and the staircase exists precisely at the finite sizes and tunable effective temperatures of current Rydberg platforms. This makes the effect directly observable in existing experiments. Our comparison also shows that the finite-size steps are not phase transitions: in the thermodynamic limit only a single phase transition survives, and the system crosses over to a defect-dominated paramagnet.

The dynamical GW self-energy approximation is a key computational tool to provide the fundamental spectrum of electronic systems. We reformulate this approximation, representing the particle and hole parts of the GW self-energy through a highly compact set of Cayley-transformed moment constraints. The Cayley transformation maps real frequencies to the unit circle, keeping the moments bounded as their order increases, ensuring numerical stability and allowing resolution to be focused on an energy range of interest. We calculate these Cayley-transformed moments via an efficient O[N$^4$] scaling contour integration, and from them, construct a Hermitian upfolded Hamiltonian with a linearly scaling dimensionality with system size. A single-shot diagonalization of this effective Hamiltonian gives an explicit full-frequency G0W0 Green's function with manifestly real poles and non-negative spectral weights. This enables quasiparticle energies, satellite features, and their spectral weights to be obtained across the full G0W0 spectrum. Comparisons with exact G0W0 calculations and convergence across the GW100 test set and the larger Chlorophyll A molecule demonstrate substantially faster and more reliable convergence with moment order than an earlier monomial-moment approach. These Cayley moment representations therefore provide a stable, compact, and systematically improvable route to the complete spectral information of zero-temperature GW, without explicit frequency grids, plasmon-pole models and other common approximations, or analytic continuation.

The microscopic origin of magnetism in CeFe$_2$ has remained unresolved for almost forty years, where polarized-neutron diffraction and x-ray magnetic circular dichroism infer markedly different Ce $4f$ spin and orbital moments, that also are in disagreement with theory. We show here that within a relativistic multi-impurity DFT+DMFT framework, where the Fe $3d$ states are treated by spin-polarized T-matrix fluctuation exchange and Ce $4f$ orbitals by a bath-coupled configuration-interaction solver, this long standing problem is resolved. This level of theory is exclusive in reproducing magnetic moments (spin and orbital) for both the Ce and Fe atoms, yielding a total moment in agreement with the measured saturation moment. The theory put forth here is much closer to the atom specific moments reported from XMCD, compared to values from polarized-neutron diffraction. The occupation $\langle n_f\rangle=0.85$ and charge variance $\delta n_f^2=0.27$ establish substantial valence fluctuations, while the spectral function simultaneously recovers significant weight at the Fermi level together with separate incoherent structures. These results identify bath-mediated polarization and configuration mixing as the essential ingredients governing the electronic structure and magnetism of CeFe$_2$.

Unconventional superconductivity typically occurs near magnetic instabilities, and the corresponding spin fluctuations are widely believed to play a crucial role in mediating electron pairing. UTe$_2$ is a promising candidate for exhibiting multiple spin-triplet superconducting phases when tuning with applied pressure and magnetic fields, but the nature of the magnetism driving these unconventional pairing states is undetermined. Our measurements of UTe$_2$ under applied pressures and magnetic fields reveal the presence of a magnetic order hidden within the pressure-induced superconducting dome, which vanishes together with the superconductivity once there is sufficiently high pressure to induce the three-dimensional antiferromagnetic phase. Extrapolation of the phase boundary of the hidden magnetic order, which is most likely antiferromagnetic in nature, points to a zero-temperature quantum critical point that coincides with the maximum transition temperature of the pressure-induced superconducting dome, suggesting that it could corresponds to the parent magnetic phase of the critical antiferromagnetic spin fluctuations driving the triplet superconductivity. These findings advance the understanding of the interplay of magnetism and superconductivity in an exemplar candidate triplet superconductor, which is necessary for revealing the microscopic origin of the different unconventional superconducting phases.

We construct an exactly solvable extension of the spin-$1/2$ Kitaev honeycomb model in which conserved $\mathbb{Z}_2$ fluxes determine not only the signs but also the connectivity of nearest-neighbor Majorana hopping. At a tuned loop point, hopping survives only across opposite-flux plaquettes, so every vertex has active degree zero or two and the matter Hamiltonian fragments in each flux sector into independent Majorana rings and isolated zero modes. Exact ring spectra and bond counting then bound the matter energy over all local flux configurations and all four Wilson-loop sectors, and split it exactly into a frustrated triangular-lattice Ising term, whose extensively degenerate ground states are the fully packed loop coverings, and a non-negative Majorana residual. On admissible commensurate tori, the residual selects precisely the three translation-related $2/3$-vison crystals, which saturate the bound, and an exact fermion-parity identity shows that for antiferromagnetic coupling their vacua also survive projection, making them rigorous ground states of the spin model. Within a single crystal, a depth-one local unitary then maps the ground space onto that of a sheared square-lattice toric code, giving fourfold topological degeneracy. The model thus realizes exact nonperturbative gauge-matter feedback: the flux fixes where the Majorana fermions may move, and their zero-point energy selects in return a topologically ordered vison crystal with spontaneously broken translation symmetry.

Kagome FeSn exhibits an occupied flat band at its terminated surface, whereas bulk FeSn adopts A-type antiferromagnetic order and does not display the same feature. Here, we combine density functional theory with primitive- and doubled-cell analysis and a double-layer tight-binding model to determine how interlayer electronic coupling and magnetic stacking control flat-band formation in FeSn. We identify an occupied Fe-$d_{z^2}$-derived flat-band manifold in the ferromagnetic state that is consistent with the experimentally observed surface feature. Brillouin-zone folding reveals that its flat branch originates from the $k_z=\frac{\pi}{c}$ sector of the primitive cell, demonstrating that it cannot be understood as an isolated kagome-layer state. Instead, the state depends on coupling between neighboring kagome layers and can be seen as a result of antibonding coupling between nearest neighbor kagome layers. A double-layer tight-binding analysis identifies interlayer Fe-Fe hopping as the dominant microscopic coupling responsible for this behavior, while a contrasting unoccupied flat-band-related manifold is governed primarily by intralayer Fe-Sn hybridization. These results establish interlayer coupling and magnetic stacking as key control parameters for kagome flat bands and highlight how coupling between layers can generate and tune extended correlated-electron states in quantum materials.

We develop an explicit plane-wave (PW) $\times$ photon-Fock approach to the quantized, velocity-gauge Pauli–Fierz Hamiltonian for periodic, first-principles calculations: because the quantized vector potential is spatially uniform, the light–matter coupling reduces to an operator-valued shift of the crystal momentum, $K\to K+\hat{\mathbf A}/c$, and the existing plane-wave machinery of ordinary solid-state DFT is reused essentially unchanged. This PW$\times$Fock construction puts first-principles cavity QED of periodic solids on the same footing as the Fock-space coupled-cluster and configuration-interaction methods already developed for molecules, opening hitherto inaccessible systems—materials in a linear or chiral cavity, in particular—to first-principles plane-wave calculations. We illustrate the method with monolayer graphene in linear and chiral cavities, obtaining a polarization-selective Haldane gap together with the corresponding density-of-states, real-space, and circular-dichroism optical signatures. A full Brillouin-zone Berry-curvature calculation confirms the topological character of the chiral-cavity gap directly: the occupied manifold carries a quantized Chern number that steps through a non-monotonic sequence, $C=1\to3\to{-1}\to1\to2\to{-1}\to1$, with two narrow, sign-reversed windows—a property of extended, vacuum-dressed matter with no counterpart in a finite molecular system.

In conventional insulators, electronic charge is localized in Wannier orbitals centered on the atoms. In an obstructed atomic insulator (OAI), the Wannier orbitals sit instead in the empty voids between atoms. These displaced orbitals give rise to an analog of the topological bulk-boundary correspondence, in which a boundary mode occurs only where the lattice termination severs an orbital. However, experimentally identifying OAIs has remained challenging, because the Wannier orbital of a dispersive electronic band is not an energy eigenstate and cannot be measured directly. Here we engineer an acoustic metamaterial hosting an isolated flat band, in which the Wannier orbitals become energy eigenstates. By measuring the amplitude and phase of the acoustic pressure field, we map the orbital's $f$-like structure and locate its Wannier center in a void between lattice sites—providing the first phase-resolved image of an obstructed Wannier orbital. By altering the lattice termination, we observe the predicted boundary states. Such acoustic flat-band metamaterials offer a direct probe of single-particle ingredients such as quantum geometry, which govern correlated phenomena in electronic flat bands, including proposed routes to unconventional superconductivity.

A common belief in Kondo physics is that a magnetic impurity can act as an efficient probe of key properties of its host bath. In altermagnets, however, this intuition fails in a symmetry-enforced way: the momentum-dependent spin splitting cancels in the local impurity spectrum, making a conventional single-impurity Kondo resonance essentially blind to the altermagnetic form factor. Here, we overcome this constraint by introducing Floquet symmetry conversion. We show that an in-plane AC field converts the hidden altermagnetic spin splitting into a locally detectable spin-dependent hybridization channel, which is further amplified by Kondo correlations into a novel altermagnetic Kondo effect. Remarkably, the Kondo splitting exhibits a nontrivial dependence on the field orientation and inherits the same crystalline form factor as the altermagnetic host, thereby serving as Kondo tomography of altermagnetic spin splitting. This field-controlled response further provides a natural route to symmetry-controlled Kondo logic gates. Our results establish a field-controllable altermagnetic Kondo effect, linking symmetry-resolved impurity spectroscopy to Kondo logic functionality.

Repeated evaluation of the single-particle Green's function (GF) across parameter space is a recurring bottleneck in many-body methods, limiting the resolution at which phase boundaries may be probed and the frequency resolution of computed spectra. We introduce MOR+EC, a framework that constructs reusable reduced-order models for computing single-particle Green's functions by combining eigenvector continuation (EC) for parameter space exploration and model order reduction (MOR) for extrapolation in frequency space. Contrary to conventional parameterized MOR, we construct these reduced-order models with a parameter-independent resolvent, further reducing the number of required full-space evaluations. Benchmarking against exact diagonalization as the impurity solver for our example case of DMFT calculations for single- and two-band models, MOR+EC reproduces the DMFT-converged impurity GF to an average relative error of $\sim10^{-4}$, with a median wall-time speedup of $16-91\times$. This accuracy and efficiency together resolve a fine-grained scan of the impurity occupation as doping is tuned and produce a high-resolution phase diagram of an orbital-selective Mott transition. The reduced-order model also reproduces real- and imaginary-frequency spectra at no additional cost in full-space evaluations. This framework applies broadly to GF-based methods requiring repeated parametric evaluation and high resolution of the frequency axis.

The hunt for a material realization of quantum spin ice has motivated more than two decades of experimental effort. The candidate materials inevitably contain crystal imperfections, such as magnetic vacancies, whose effects are often disregarded. Here, we show that experimentally relevant levels of dilution can qualitatively reshape the low-energy behavior, as nearby vacancies generate quantum fluctuations that are absent in the clean system. Already at dilution levels as low as two percent, well below those reported in cerium-based pyrochlores, these vacancy-induced processes connect percolating clusters of spins and dominate over the conventional quantum-spin-ice dynamics. We therefore argue that magnetic vacancies in current experiments can strongly contaminate, and potentially completely obscure, the sought-after signatures of quantum spin ice. We support these conclusions using large-scale, unbiased quantum Monte Carlo simulations and exact diagonalization.

Pair-density-wave (PDW) superconductors admit half-quantum vortices that can bind Majorana zero modes, but whether such defects are energetically stabilized in microscopic models remains unclear. We address this question in a spinless honeycomb-lattice model with a PDW phase. Microscopic Hartree-Fock calculations determine the superfluid stiffness $\rho$ and PDW relative-phase stiffness $\kappa$, and show that $\kappa/\rho$ approaches unity near the continuous PDW–Dirac-semimetal transition, strongly reducing the long-wavelength cost of vortex fractionalization. Combining this with microscopically extracted Ginzburg–Landau couplings, we show that vortex-core energetics favor fractionalization, producing a strongly enhanced splitting scale and a field-driven full-vortex–to–half-vortex lattice transition. We determine the resulting two-flavor half-vortex lattice structure and construct the associated Majorana lattice. Majorana hybridization produces geometry- and flux-dependent bands with Dirac nodes and zero-energy Fermi lines. Together, these results establish a microscopic route from PDW superconductivity to field-induced half-vortex and Majorana lattices.

Pair-density-wave (PDW) order is a superconducting state with a spatially modulated order parameter and is generally subleading to uniform superconductivity within the conventional weak-coupling BCS paradigm. Here, using a twisted bilayer checkerboard-lattice model, we show that momentum-space nonsymmorphic symmetry provides a generic mechanism that can instead promote PDW order to a leading weak-coupling instability. Combining a controlled Wilsonian renormalization-group analysis at charge neutrality with a finite-doping Bethe–Salpeter analysis, we determine the leading ordering tendencies among various competing instabilities. At charge neutrality, two symmetry-related quadratic band touchings support spin-singlet and spin-triplet PDW instabilities for different attractive interactions, whereas repulsive interactions favor quantum Hall insulators and finite-$\mathbf Q$ density-wave orders. Upon doping, the nonsymmorphic symmetry, together with time reversal, protects the Cooper logarithm in the finite-momentum $\mathbf Q$ pairing channel at generic fillings, allowing PDW order to remain a leading instability over the broad doping range studied. This mechanism extends naturally to moiré Chern bands: by breaking time-reversal symmetry while preserving the nonsymmorphic symmetry and inversion, we obtain a fully gapped topological spin-triplet PDW state with BdG Chern number $C_{\text{BdG}}=8$. Our results establish momentum-space nonsymmorphic symmetry as a general weak-coupling route to PDW superconductivity, including topological PDW states.

We study the stimulation of superconductivity by an external electromagnetic radiation — the Eliashberg effect — in a disordered $d$-wave superconductor. We use the self-consistent Keldysh–Nambu quasiclassical formalism augmented by an inelastic relaxation term to compute the static correction to the pairing amplitude by treating elastic scattering within the Born approximation with the full second-order impurity vertex retained. We find that the clean $d$-wave superconductor shows no enhancement at any frequency: without a momentum relaxation channel a spatially uniform drive produces no absorption, only pair breaking. Elastic impurity scattering restores absorption and with it activates response in the Eliashberg channel. We find enhancement of the pairing amplitude which is confined to a bounded window in frequency, disorder strength, inelastic scattering rate and gap magnitude. Both edges of the window scale with the gap but are set by the competition between quasiparticle redistribution, heating and pair breaking rather than by a feature of the spectrum. Furthermore, in contrast to the $s$-wave when the threshold is pinned at $2\Delta$, the upper edge is not pinned to the maximum gap and crosses it as the system approaches the critical temperature.

We study magnetic systems featuring competing antiferromagnetic and spin-nematic phases, described by dipolar primary and quadrupolar secondary order parameters. While the antiferromagnetic phase breaks time-reversal and spin-rotational symmetries, only spin-rotational symmetry is broken in the nematic phase, which can be understood as a spin-vestigial phase. We develop a classical continuum field theory with independent vector and tensor fields and use mean-field and renormalization group methods to analyze its phases and finite-temperature transitions. We determine the fixed-point structure using an $\epsilon$ expansion about the upper critical dimension of six and track the resulting fixed points to lower dimensions using a perturbative fixed-dimension renormalization group approach. The multicritical fixed point governing the meeting of the antiferromagnetic, nematic, and paramagnetic phases occurs at imaginary coupling throughout the dimensions accessible to our analysis, indicating a first-order transition through the triple point. Away from the triple point, a direct paramagnetic-to-antiferromagnetic transition can be continuous when the tensor mass is sufficiently large, without an intervening vestigial phase. We argue that it is governed by the cubic universality class in $d=3$ and the Ising universality class in $d=2$ for three-component order parameters. The theory also supports a two-step transition with an intermediate spin-nematic phase. The paramagnetic-to-nematic transition is governed by the four-state Potts universality class in $d=2$ and is first order in $d=3$, while the nematic-to-antiferromagnetic transition is generically expected to be continuous and of Ising type in both dimensions. Our results provide a field-theoretical framework for understanding the finite-temperature transitions observed in the candidate Kitaev material Na$_2$Co$_2$TeO$_6$.

Spin-density wave (SDW) order and superconductivity frequently compete and coexist in unconventional superconductors, where spin fluctuations often mediate superconducting pairing. In iron-chalcogenide superconductors, FeSe$_{1-x}$S$_x$, SDW order has only been detected under applied pressure, while both spin and nematic fluctuations are involved in determining their rich superconducting phase diagrams. Here, we report evidence for an incipient SDW phase, within the nematic state of FeSe$_{1-x}$S$_x$, revealed in magnetic fields up to 68~T. Once superconductivity is quenched, we observe sharp upturns in longitudinal resistivity accompanied by anomalies in tunnel diode oscillator frequency response and torque anisotropy, consistent with a field-induced electronic order. Dominant low-frequency quantum oscillations reveal a small reconstructed Fermi surface, consistent with a field-induced SDW order. Direct experimental comparisons with a pressure-tuned nematic, analogue, FeSe$_{0.96}$S$_{0.04}$, demonstrate that SDW phases are stabilized within the nematic phase of FeSe$_{1-x}$S$_x$ via both chemical substitution and applied pressure. These findings reveal that by weakening nematicity, the SDW orders are stabilised, which promotes the dominant superconducting pairing mechanism in iron chalcogenides.

Easy-axis frustrated triangular lattice antiferromagnets provide an important playground for stabilising a wide range of exotic magnetic phases. The delafossite $2H$-AgNiO$_2$ offers a unique model system containing a lattice of localised ($S=1$) moments surrounded by a honeycomb of itinerant electrons. Below $T_{\rm N} =19$ K, the system exhibits collinear stripe antiferromagnetic order, whereas applied magnetic fields induce a cascade of transitions which has been proposed to contain a magnetic supersolid phase. In this study, we perform detailed angular and field-dependent torque measurements in static fields of up to 45~T on single crystal samples. The angular dependence of the torque displays a sawtooth-shaped signal close to the first supersolid phase, while near $T_{\rm N}$, an unexpected additional modulation emerges. On the other hand, the field dependence of the torque indicates the presence of four field-induced anomalies which evolve in distinct ways as a function of field orientation. To understand these complex behaviours and assess the role of local moments, we employ mean-field and Monte-Carlo calculations on a minimal spin model and construct comprehensive polar phase diagrams at different temperatures. We find that the angular dependence of the torque can be understood in terms of crossing different phase boundaries by field rotation, and we identify qualitative similarities between the experimental and theoretical polar phase diagrams. Our study highlights $2H$-AgNiO$_2$ as a rich anisotropic system that provides a robust example of how spin supersolid orders can manifest in angle-dependent magnetic torque.

We investigate charge-density-wave (CDW) coarsening in a two-dimensional quasiclassical Holstein model following thermal quenches into the ordered phase. Although the staggered CDW order parameter is nonconserved, domain-wall motion remains constrained by conservation of the microscopic electronic charge. The simulations exhibit apparent growth exponents between $1/4$ and the Allen–Cahn value $1/2$. These apparent exponents are primarily accounted for by the crossover kinetics $\dot{L}=[D(T)/L][1+L_\times^2(T)/L^2]$, where $L_\times(T)$ is a temperature-dependent crossover length. At low temperature, nearly binary occupations require compatible wall segments to rearrange cooperatively, producing the $L(t)\sim t^{1/4}$ limit. Thermal broadening creates partially occupied interfacial sites that permit local curvature-driven motion and restore $L(t)\sim t^{1/2}$ at late times. Fits to the measured growth rate, a dimensionless rate collapse, and a long-time large-system simulation consistently support this crossover picture. These results show that a microscopic conservation law can generate long-lived anomalous coarsening even when the emergent order parameter is nonconserved.

The realization of an intrinsic anomalous Hall effect (AHE) in the absence of bulk magnetism is a rare phenomenon, requiring a spontaneous breaking of the time-reversal symmetry within the boundary states without a thermodynamic phase transition. Here, we report a robust, zero-field-hysteretic intrinsic AHE confined to the low-temperature surface-conduction regime of the prototypical narrow-gap insulator FeSi. By systematically investigating single crystals grown via Czochralski and chemical vapor transport methods with controlled thicknesses and surface preparations, we demonstrate that low-temperature electrical conductivity correlates with surface roughness and anti-correlates with sample thickness, confirming the emergence of surface conducting states (CSS) below $T_{\rm CSS} \simeq 55-75\text{ K}$. Meanwhile, a robust, field-hysteretic and temperature-independent anomalous Hall conductivity is found below $T_{\rm AHE}\simeq45-70\text{ K}$, implying the presence of magnetic order in the surface conduction regime. Bulk magnetic susceptibility and specific-heat measurements reveal no thermodynamic phase transitions, verifying that the sample interior remains a non-magnetic insulator. Analyses of conductivity scaling and effective three-dimensional conductivity reveal the intrinsic nature of this surface-driven AHE, evidencing the presence of an emergent magnetic order within the metallic surface of a non-magnetic bulk insulator. These findings establish FeSi as a compelling platform to investigate the interplay between strong electron correlations and anomalous Hall transport.

The precise and efficient evaluation of large-scale lattice sums involving power-law kernels is a fundamental computational problem in the simulation of classical and quantum systems with long-range interactions. While methods for spatially isotropic kernels, some based on Epstein zeta functions, have advanced considerably in recent years, the anisotropic case has lagged behind, despite its broad relevance to both fundamental and effective interactions such as the dipole interaction in magnetic materials. In this work, we solve this issue by defining and analyzing anisotropic Epstein zeta functions for which we derive stably computable representations obtained from wave vector derivatives of lattice sums over isotropic interaction kernels. These functions find direct application in the analytical and numerical study of anisotropically interacting lattice systems. Going further, they provide the correction term in an exact equivalence between discrete lattices and their continuous analogs in a recent generalization of the classical Euler-Maclaurin summation formula to lattices and summands involving power-law kernels. Their connection to high-order derivatives of zeta functions can be used to improve convergence rates of numerical algorithms, for instance in micromagnetics, or to provide rapidly convergent expansions suitable for precomputations of generalized zeta functions. We derive a stably computable representation of anisotropic Epstein zeta functions, including the possibility for analytically removing Rayleigh–Wood singularities, and we develop a numerical algorithm for their stable evaluation for any lattice, power-law decay exponent and anisotropy order. We benchmark the algorithm against closed-form identities, direct summation and multi-precision results, obtaining machine precision across various lattices, power-law exponents, and anisotropy orders.

We introduce a class of $2d$ quantum spin systems based on a unitary spherical fusion category with a chosen object. These models have frustration-free, reflection positive, but generally non-commuting local interactions, generalizing the Levin-Wen string-net models. Based on the theory developed in arXiv:2510.20662, we explicitly realize the Temperley-Lieb-Jones algebra, and more generally fusion spin chains as their boundary algebras.

Orbital degrees of freedom play a pivotal role in shaping the physical properties of two-dimensional (2D) van der Waals magnetic systems, strongly influencing electron-phonon coupling and intermediate-state dynamics. In this study, we present a comprehensive temperature and thickness-dependent Raman investigation of the single crystals of 2D van der Waals antiferromagnetic series (NixFe1-x)2P2S6. Utilizing Raman spectroscopy, we explore the interplay between local orbital excitations and lattice vibrations, observing higher-order phonon modes extending up to the fourth order. We observe an anomalously high and weakly temperature-dependent intensity ratio of these higher-order modes relative to low-energy first-order phonons. Theoretical cluster calculations and Franck-Condon modelling reveal that these features originate from resonantly enhanced multiphonon scattering mediated by localized intermediate Ni 3d8 multiplet excitations. The local orbital occupancy of these intermediate states couples strongly to lattice coordinates, providing a selective enhancement mechanism for specific phonon channels. Notably, these higher-order features are absent in the end-member Fe2P2S6. This distinction reflects the charge-transfer character of Ni2P2S6, which places optical transitions in resonance with local multiplet states, contrasted with the Mott-Hubbard insulator regime in Fe-rich analogues. Our findings clarify the microscopic origin of high-frequency Raman scattering in transition metal thiophosphates and underscore the central role of local orbital-phonon interactions in 2D correlated magnets.

We present a unified study of charge and spin qubits encoded in a single interacting quantum dot tunnel-coupled to Rashba fermionic leads. The dot is described by an Anderson impurity Hamiltonian with either repulsive or attractive local interactions and a magnetic field of arbitrary orientation. In the repulsive regime, a spin qubit is encoded in the singly occupied spin sector, whereas in the attractive regime, close to the degeneracy between the empty and doubly occupied configurations, these two states define a charge-qubit subspace. We combine a weak-coupling Lindblad master equation in the Markovian secular limit with numerically controlled matrix-product-state simulations of the full dot-reservoir system. In equilibrium, we identify magnetic pair breaking in the attractive regime and a weak Rashba-induced magnetic anisotropy when the magnetic field is rotated relative to the spin-orbit axis. In the dynamical regime, relaxation and decoherence are controlled by the energetic gap between the logical manifold and nearby leakage states, and are further enhanced by Rashba-dependent tunneling. These findings show that even a minimal Anderson-impurity description captures key ingredients for coherent spin and charge qubits: the energetic structure of leakage states and spin-orbit-dependent dot-lead hybridization.

The complex interplay between spin-orbit coupling, magnetism, and magnetic field at the interface of a heterostructure consisting of ferromagnet (FM) and heavy metal (HM), often exhibit extraordinary magnetic and electric phenomena where an in-plane Dzyaloshinskii-Moriya (DM) interaction plays a crucial role to stabilize local spin texture in FM layer. Here, we report detailed magnetic and magneto-transport behaviour on an epitaxially grown thin heterostructure with 3$d$ FM La$_{0.67}$Ca$_{0.33}$MnO$_3$ (LCMO) and 5$d$ HM SrIrO$_3$ (SIO). Magnetic measurements show an unusual development of magnetic ordering in SrIrO3 around 42 K, which further leads to a Mn/Ir magnetic coupling at the interface. The magnetoresistance (MR) measurements show an evolution of its value and shape with the magnetic state of this bilayer. While MR is negative at high temperature, it shows a positive to negative crossover with stable magnetic ordering of LCMO, and finally the positive MR exhibits an asymmetry at low temperature with the ordering of SIO. While we ascribe this unusual MR behaviour to interface-driven varying spin scattering between itinerant and localized electrons, our results shed a light to comprehend the complex but tunable interface behavior on charge transport in a particularly designed heterostructure, offering valuable insights for future functional material engineering.

The fate of average symmetry-protected topological (ASPT) states based on the one-dimensional cluster state is investigated by using the Choi mapping, namely, the doubled Hilbert-space formalism. By introducing two effective spins, $\tau$ and $\eta$, on each doubled rung, we obtain a transparent representation of the ASPT parent Hamiltonian and systematically identify the conserved stabilizers and the corresponding orders. We further study symmetry-preserving operations that deform the ASPT by combining qualitative effective-Hamiltonian and systematic parent-Hamiltonian analyses with numerical matrix-product-state filtering calculations. We find that although the ASPT remains robust over a broad range of decoherence strengths, strong-to-weak spontaneous symmetry breaking (SWSSB) becomes exact in the maximal-decoherence limit. In addition, we consider symmetry preserving no-click postselection, which removes the exact conservation law supporting the Rényi-2 string order of the ASPT and drives the system toward weak-symmetry spontaneous symmetry breaking (WSSB). Again, the ASPT remains robust over a broad range of postselection strengths, with WSSB becoming pronounced only near the projective limit and exact at the limit itself.

The quantum anomalous Hall effect carries dissipationless chiral edge currents without an external magnetic field, yet raising its operating temperature and controlling the number of edge channels remain difficult. Using first-principles calculations, we identify the two-dimensional metal-organic kagome ferromagnet Eu$_2$(C$_6$H$_4$)$_3$ as an intrinsic Chern insulator whose topological gap can be enlarged by mechanical strain. The monolayer has a spin-orbit-coupling-induced gap of 72.7 meV that widens to 124.7 meV under -8% biaxial strain, realizing a quantum anomalous Hall phase with Chern number $\mathcal{C}=-1$ and a single chiral edge state. The local moments come from the half-filled Eu $4f^{7}$ shell, while the gap-opening spin-orbit coupling is carried by Eu $5d$ states hybridized into the carbon kagome bands. The AB-stacked bilayer couples ferromagnetically and accumulates the per-layer Chern numbers, giving $\mathcal{C}=-2$ with two co-propagating chiral channels. An out-of-plane electric field then drives the bilayer through a sequence of topological transitions among $\mathcal{C}=-2$, $-3$, and $-1$, switching the number of edge channels. Together, strain, stacking, and gating give three distinct handles on the gap and the Chern number within a single stoichiometric material.

We show that the noncommutative second Chern number of a $(3+1)$D disordered axion pump remains quantized beyond global spectral gap closure at $W_g \approx 14.5$. Large-scale computation of the second Chern number and finite-size scaling demonstrate convergence of $\mathrm{Ch}_2$ toward $-1$ well into the mobility-gap regime ($W \lesssim 16.5$), while the Středa-Hall response $\partial_\phi \mathrm{Ch}_{0,3}$ departs rapidly after global spectral gap closure, serving as an internal control that distinguishes bulk mobility-gap protection from finite-size artifacts. Level statistics identify a 3D unitary Anderson transition at each pump slice and locate the mobility-edge bottleneck at $\tau=0$, with critical disorder $W_c \approx 18$.