arXane › Physics › Condensed Matter
Wednesday, 4 November 2026: 16 new papers, 13 cross-lists and 14 replacements in Strongly Correlated Electrons (cond-mat.str-el), in arXiv's order, with full abstracts. The same papers as arXiv's own listing, set as a newspaper; every title links to arXiv.
A defining feature of quantum materials is that multiple orders govern low-energy physics and are not independent. We study Bi$_2$Se$_3$ by combining DFT with a renormalized correlated honeycomb model in which frustrated magnetic order and helical topological surface states are coupled via one control parameter. The surface states map to a honeycomb Hubbard model with frustrated $J_1$--$J_2$ exchange. Exact diagonalization up to 20 sites shows the N\'{e}el structure factor and valence-bond-solid order parameter cross at $J_2/J_1 \approx 0.22$, agreeing with QMC/DMRG, and a dynamical spin structure factor broadens near the crossover, as expected for a spinon continuum. Band inversion of the renormalized tight-binding model occurs on the same critical locus, producing jumps in the Chern number and $\mathbb{Z}_2$ invariant mirrored by the skyrmion charge $Q$. This gives a microscopic link: $Q$ selects the axion angle and thus the topological magnetoelectric coupling. We distinguish axion coupling, independent of skyrmion helicity, from the helicity-dependent magnetoelectric multipole coupling, whose toroidal component scales as $\sin\gamma$ and vanishes for N\'{e}el-type textures. We derive the $Q$-topological magnetoelectric energy and estimate $\sim 10^{-20}\,\mathrm{J}$ per skyrmion per cycle for few-tesla fields. The cycle is thermodynamically bounded: constant-$\theta$ cycles extract no net work, and efficiency is limited by axionic entropy change.
Orthogonal metals provide a paradigmatic example of strongly entangled metallic states whose transport and thermodynamic properties resemble those of conventional Fermi liquids, while their single-electron excitations remain fundamentally distinct. Despite considerable interest in their unusual ground-state properties, orthogonal metals in three spatial dimensions and their finite-temperature behavior remain relatively unexplored. Here, we investigate a three-dimensional orthogonal metal and characterize the thermodynamic and spectroscopic signatures associated with its finite-temperature phase transition. Starting from a simple model of fermions coupled to spin degrees of freedom, we perturbatively demonstrate that the thermal transition known to occur in the purely bosonic limit persists in the presence of coupling to a gapless Fermi surface. We then examine physical observables that change prominently between the coherent and orthogonal-metal regimes. In particular, we calculate the evolution of the physical-electron spectral function and identify characteristic signatures in angle-resolved photoemission spectroscopy. We find a pronounced contrast in low-energy spectral weight between the coherent and orthogonal-metal regimes without requiring conventional symmetry-breaking order. Our results establish finite-temperature orthogonal-metal physics as a possible mechanism for pseudogap-like behavior in three-dimensional and quasi-two-dimensional layered materials with non-negligible interlayer hopping, which may be applied to the recent experiments in $\mathrm{Sr_2 VO_3 Fe As}$.
Collective modes provide a powerful probe into the properties and stability of topologically ordered and strongly interacting phases of matter, such as fractional quantum Hall states. Yet, the description of fractional-state excitations away from the Landau-level limit remains a formidable challenge. We develop a framework for describing collective excitations in the strong-coupling regime of coupled-wire constructions and show that they emerge as solitons and breathers of effective sine-Gordon theories. This approach provides a systematic route to studying collective modes in a broad class of fractional states. Applied to a coupled-wire construction of the fractional quantum Hall effect, the framework captures key features of the magnetoroton branch. It naturally extends to fractional Chern insulators, demonstrating that magnetoroton-like collective modes persist well beyond the Landau-level limit. We find that the magnetoroton gap increases as the Fubini-Study metric approaches the ideal (trace-condition) limit, highlighting the important role of quantum geometry in the stability of fractionalized phases and their collective excitations. The same trend favors the stability of the long-wavelength quadrupolar mode associated with the chiral graviton. Together, these results identify a distinct interplay between fractionalization and quantum geometry, and provide an analytical framework for studies of collective excitations in fractional topological matter.
Strong electron correlations and topology offer complementary routes to controlling electrical conduction, as correlations can make electrons heavy (e.g. Kondo lattices) whereas topology can make them behave as massless particles (e.g. Dirac or Weyl systems), and having both in one material is rare. In Kondo lattice systems, Kondo hybridization between localized 4$f$ and conduction electrons strongly enhances the quasiparticle mass, where in Weyl-Kondo systems these Kondo-renormalized bands form Weyl states, and simultaneous signs of both Kondo and Weyl states in one material have not been observed in transport. Here we report signs of both in the kagome metal \ce{Yb_yCo3Ge_{3-x}Sn_x} by combining magnetotransport, heat capacity, magnetization, angle-resolved and X-ray photoemission spectroscopy, and DFT+U calculations to reveal Yb-dependent Kondo scattering developing into lattice coherence, with extrapolated Sommerfeld coefficient of approximately 2 ~Jmol$_{\mathrm{Yb}}^{-1}$K$^{-2}$. Transverse magnetoresistance (MR) follows single-ion Kondo scaling, whereas longitudinal transport contains an additional negative response proportional to B$^2$ and remains unsaturated up to 32 T, consistent with a chiral anomaly. These findings support a picture of Kondo and Weyl-like conduction arising from distinct electronic states without external Fermi-level tuning, suggesting a possible route to combining correlated and topological functionality in a bulk material.
We show that a microscopic model of twisted MoTe$_2$ with screened Coulomb interactions produces topological superconductivity. Using the density matrix renormalization group (DMRG) on infinite cylinders, we find that the narrow Chern band of twisted MoTe$_2$ has Cooper pair correlations that strengthen with cylinder circumference, consistent with two dimensional superconductivity. The superconductor has chiral $f$-wave pairing around the valley center, and its topology produces chiral Majorana edge modes and non-Abelian vortex cores. At zero displacement field, the superconductor spans fillings $-0.78\lesssim\nu\lesssim-0.72$, close to the experimental range, and extends in a dome to finite displacement field. We then predict how its stiffness evolves with the filling and the tunable displacement field. The interplay with screening length is also examined. Nearby, we find a fractional Chern insulator, a topological charge density wave, a metal, and a charge-ordered state. The last is a candidate for the reentrant integer Hall regime in experiments. These results establish a route from repulsive interactions in microscopic models of moir\'e materials to chiral topological uperconductors with chiral Majorana edge modes.
The Korringa factor $K(\alpha)$ in the nuclear magnetic resonance studies is a widely used measure of electron-correlation effects in metals and is conventionally interpreted using the non-correlated value $K(\alpha)$ = 1. In Dirac-fermion systems, however, the non-correlated reference value depends on the electronic density of states (DOS) and differs from that of conventional metals. Here, we theoretically investigate the non-correlated Korringa factor $K^*(\alpha)$ in a Dirac nodal-line (DNL) system with finite nodal-line dispersion using a DOS-based approach. We show that $K^*(\alpha)$ exhibits an intrinsic temperature dependence, continuously evolving from the Dirac-fermion value of 1.71 at high temperatures to the metallic value of 1 at low temperatures. The crossover temperature is found to be proportional to the nodal-line dispersion width, identified as the characteristic energy scale governing the non-correlated Korringa factor in DNL systems. We further demonstrate that Landau quantization generates singular DOS structures that strongly enhance $K^*(\alpha)$, producing pronounced peaks even in the absence of electron correlations. In addition, $K^*(\alpha)$ exhibits two distinct types of magnetic oscillations arising from intra-level and inter-level contributions. The latter originates from the overlap of singular points belonging to positive and negative quantum-number Landau subbands at the Fermi level and represents a unique consequence of the finite energy dispersion of a DNL. These results provide a quantitative reference for interpreting NMR experiments in DNL materials and for identifying genuine correlation effects beyond DOS-induced contributions.
Neutron scattering provides microscopic information on magnetic order and spin dynamics. Most experiments, however, use unpolarized neutrons and do not fully exploit the information carried by the neutron spin. Longitudinal polarization analysis (LPA), established in the pioneering work of Moon, Riste, and Koehler at Oak Ridge National Laboratory in the late 1960s, separates magnetic and nonmagnetic scattering contributions through their different effects on the neutron spin. In this review, we illustrate how LPA can distinguish weak magnetic scattering from nonmagnetic contributions, constrain small moment components, and resolve the spin-space anisotropy of magnetic excitations. We introduce the formalism connecting measured polarization channels to magnetic quantities and discuss scattering geometry, crystallographic projections, and corrections for finite polarization. Our aim is to provide a practical guide for neutron scatterers using LPA to determine magnetic structures and characterize spin excitations in quantum materials. We conclude with opportunities in altermagnets, unconventional superconductors, and kagome magnets.
Neural quantum states provide accurate variational representations for interacting lattice fermions and spins. Turning a new ansatz into a reproducible calculation, however, requires coordinated implementations of the Hamiltonian, sampling, optimization, observables, and accelerator parallelism. We present LaQX (Lattice Quantum simulation based on jaX), an open-source neural quantum state library based on JAX that organizes these components through common functional interfaces. Beyond ground-state variational Monte Carlo, LaQX supports excited-state calculations, Green's Function Monte Carlo refinement, adiabatic evolution, and real-time evolution with time-dependent variational Monte Carlo. It consolidates methods developed in recent high-accuracy neural quantum state studies of the Hubbard model and frustrated magnets, and the package has been used to investigate the triangular-lattice Hofstadter-Hubbard model. We document these capabilities with reproducible calculations for Hubbard, $J_1$-$J_2$ Heisenberg, altermagnetic Hubbard, and interacting Hofstadter models. Function-oriented modules separate the scientific components and limit the source context needed for extensions by human developers and large language models. Source code, documentation, and executable examples are available at https://github.com/bytedance/laqx.
The Yb delafossites NaYbSe$_2$, KYbSe$_2$, CsYbSe$_2$ and NaYbO$_2$ are candidates for the U(1) Dirac spin liquid (DSL) of the triangular lattice. Strong spin-orbit coupling gives their exchange an XXZ anisotropy $\Delta$ and bond-dependent couplings $J_{\pm\pm}$, $J_{z\pm}$ that lock the spin frame to the lattice. We show that, within a single layer of a stable Heisenberg DSL, these couplings generate no relevant Lorentz-scalar operator of their own. Inversion at the bond centers removes the Dzyaloshinskii-Moriya channel that gaps the kagome DSL, so the locked symmetry forbids a mass, density or current at any order and, assuming continuity, any new monopole term through charge three. Every Lorentz-scalar four-fermion operator induced by spin-orbit coupling shares an SU(4) multiplet, and hence its scaling dimension, with a Heisenberg-allowed one, and the nine non-scalar quartics without such a partner arise only at second order and are irrelevant at large $N$. The Heisenberg DSL itself allows a Lorentz-vector quartic of large-$N$ dimension 2.92, which a stable phase must also render irrelevant. Beyond a single layer, spin-orbit coupling opens an interlayer monopole channel in rhombohedral stacking. If the Heisenberg DSL is instead multicritical, an anisotropy as small as that of KYbSe$_2$ matters only below tens of mK. At the transition to 120$^\circ$ order the anisotropy is relevant, and exact diagonalization indicates that easy-plane anisotropy selects the chiral-Ising class. Existing KYbSe$_2$ neutron data below $J$ do not yet fix the K-point exponent, and gapless out-of-plane spin fluctuations at the K point would test the chiral-Ising selection.
The Yb delafossites NaYbSe$_2$, KYbSe$_2$, CsYbSe$_2$ and NaYbO$_2$ are candidates for the triangular U(1) Dirac spin liquid, QED$_3$ with $N_f=4$, but their exchange is spin-orbit coupled. Under their spin-orbit-locked space group we determine which operators the XXZ anisotropy and the bond-dependent couplings $J_{\pm\pm}$, $J_{z\pm}$ induce, and at what order. Symmetry forbids every Dirac mass, density and current at any order and, assuming adiabatic continuity, any new monopole term through charge three. At linear order the couplings reach only spin-2 members of the quartic multiplets $\mathbf{20}'$ and $\mathbf{84}$, which share their dimensions with Heisenberg-allowed operators. At second order $J_{\pm\pm}$ and $J_{z\pm}$ renormalize the anisotropy through $J_{z\pm}^2-2J_{\pm\pm}^2$, and nine spin-1 quartics without Heisenberg partners appear, irrelevant at $O(1/N)$. A single layer of a stable Heisenberg spin liquid thus acquires no relevant Lorentz-scalar operator from spin-orbit coupling. The Heisenberg liquid itself allows a Lorentz-vector $\mathbf{20}'$ quartic of large-$N$ dimension 2.92, with two-loop $\epsilon$-expansion estimates 2.9-3.5. Rhombohedral stacking adds triplet-monopole tunneling between layers at first order. At the transition to 120$^\circ$ order the anisotropy is relevant, with crossover exponent $y_T\simeq0.74$-1, and exact diagonalization shows that easy-plane anisotropy selects the chiral-Ising class. The out-of-plane spectrum at the K point then stays gapless, and the spin-flip to non-spin-flip ratio grows as $\omega^{-0.56}$ at leading order. Existing KYbSe$_2$ neutron data below $J$ do not fix the K-point exponent. In-plane fields induce a chiral mass and an out-of-plane moment proportional to $\sin3\varphi$, zero along the bonds and canceling between CsYbSe$_2$ layers, which the planar thermal Hall effect can test.
Kagome antiferromagnets are predicted to host exotic field-induced phases, yet experimental identification of their thermodynamic signatures remains challenging. Here we combine specific heat ($C$) and ultrasound measurements up to 36 T and down to 0.5 K to map the $H-T$ phase diagram of the anisotropic kagome magnet Y$_3$Cu$_9$(OH)$_{19}$Cl$_8$. We show that the suppression of long-range antiferromagnetic order with field at $\sim 15$ T approximately coincides with the onset of the unconventional $1/6$ (or $1/9$) magnetization plateau previously observed in this system. The attenuation (and sound velocity) then intriguingly increases down to 0.5 K just at $\mu_0H = 15$ T, and $C/T$ becomes temperature independent. Moreover, our measurements are consistent with the opening of a spin gap $\Delta_0\simeq3.5\pm 0.3$ K within the plateau and reveal a further compressible (ungapped) phase beyond the plateau phase, unveiling a rich sequence of field-induced phases in this quantum magnet.
In this paper we propose an ensemble model based on a swarm of dense neural networks, able to predict Heisenberg exchange interactions within less than 1% error. The model uses the inputs of the ab-initio Schr\"odinger equation, i.e. the compound structure and chemical composition. In this first work, we trained the model on a few compounds of the hexagonal manganite family and were able to infer, with similar accuracy, the J values for other compounds of the same family at randomly chosen geometries, thus showing that we accurately learned the effect of the chemical composition and structure on effective magnetic integrals J.
Strongly correlated matter without quasiparticles is central to many-body physics, quantum chaos, and quantum gravity, motivating a considerable effort toward its realization in tabletop experiments. Two challenges remain: laboratory platforms are open systems, so conformal behavior must survive dissipation, and it must be identified through measurable quantities. We address both challenges in the Yukawa-Sachdev-Ye-Kitaev (YSYK) model, in which bosons and fermions interact as in, e.g., light-matter systems, but through random all-to-all couplings that drive the boson to criticality without fine tuning. Solving the model in real time using the Schwinger-Keldysh formalism, we treat closed and open systems within a unified framework and, in both cases, consider a thermal steady state to map their phase diagrams. In addition to the known conformal and impurity (or SYK$_2$) regimes, we identify novel high-temperature regimes in which the fermions are driven by an essentially bare boson and show that their dynamics is captured by a quadratic model with time-dependent random hopping. Across all regimes, the fermionic softening of the boson is bounded by a ``criticality budget'' determined only by the Yukawa coupling and the temperature. Coupling the boson with a thermal environment induces a mass shift that deforms the boundaries between different regimes and exhausts the criticality budget, thus imposing a bound on temperature and dissipation rate compatible with self-tuned criticality. We further introduce a set of markers built from the two-point functions that separate all identified regimes, are accessible in linear response, and require no fit of the conformal exponents. We complement them with the quantum Fisher information, deriving upper bounds with and without dissipation. These results may help characterize holographic quantum matter beyond the closed setting.
The absence of magnetic Bragg peaks and a broad excitation continuum are commonly recognized experimental features of a quantum spin liquid. The Ce-based triangular-lattice hexaaluminate CeMgAl$_{11}$O$_{19}$ exhibits both signatures, yet its effective model and ground state remain under debate. Experiments have variously suggested a quantum spin liquid, proximate umbrella point, and disorder-suppressed magnetic order. Here we trace these contradictions to an overlooked multipolar degree of freedom: the transverse pseudospin of the $|\pm5/2\rangle$ Kramers doublet is a rank-5 triakontadipole rather than an ordinary dipole. Analyzing the magnetization, neutron spectra, and thermodynamics on equal footing, we establish a dipole-triakontadipole XXZ model with $J_{\perp} \simeq 0.65$ K and $J_c \simeq -0.13$ K. The resulting planar triakontadipolar superfluid order is hidden from dipolar probes, explaining the absence of a magnetic Bragg peak in neutron scattering. The zero-field excitations separate into a low-energy triakontadipole wave and a broad higher-energy continuum. We further propose nuclear spin-lattice relaxation and spin-current experiments to probe the gapless excitations of this hidden triakontadipole superfluid. Our findings thus open a new avenue for high-rank multipolar physics in rare-earth triangular-lattice magnets.
The structural, electronic, and physical properties of previously unexplored layered tetragonal compound SrMn$_2$Ge$_2$ are reported. The compound crystallizes in the ThCr$_2$Si$_2$-type structure with a crystallographic parameters $c/a$ ratio of $2.535(3)$, significantly smaller than those of the related BaMn$_2$$Pn_2$ compounds ($Pn =$ P, As, Sb, Bi), indicating enhanced interlayer interaction between the moment-bearing Mn-ions. Magnetic susceptibility measurements suggest an antiferromagnetic ground state with a high Ne\'{e}l temperature $T_{\rm N} > 350$~K\@. A large and positive magnetoresistance (MR) of approximately $50\%$ is observed at low temperatures, which follows a power-law field dependence with exponent $n = 1.50(8)$. Low-temperature electrical resistivity data reveal Kondo-like features. Heat capacity measurements show no signs of a phase transition below 300~K and further confirm a metallic ground state. Electronic structure calculations reveal a three-dimensional Fermi surface and suggest the presence of substantial electronic correlation effects.
The spin-1/2 kagome Heisenberg antiferromagnet is a central model in the study of quantum spin liquids, yet its ground-state properties remain unresolved. We perform large-scale variational Monte-Carlo calculations using neural-network quantum states (NQSs) with kagome-geometry-aware message-passing convolution on two-dimensional tori containing up to 300 spins, and achieve exceptionally low variational energies for the kagome model. The spin and dimer structure factors show no evidence of magnetic or valence-bond long-range order. Moreover, the dominant symmetry-resolved spin and dimer correlations exhibit a common scaling behavior consistent with the emergent $SO(6)$ monopole multiplet of the Dirac spin liquid. Finally, the fidelity of the optimized NQSs with Gutzwiller-projected mean-field states increasingly favors the Dirac state over the competing $Z_{2}$ candidates as the system size grows. Together, these complementary results provide evidence for a $U(1)$ Dirac spin-liquid ground state in the kagome Heisenberg antiferromagnet.
This chapter accompanies the lectures on Hartree--Fock theory and on basis sets and molecular integrals at the \href{https://www.esqc.org}{European Summer School of Quantum Chemistry (ESQC) 2026}. Intended for doctoral students, it develops the single-determinant description of electronic structure from antisymmetry and the variational principle to the orbital equations and their finite-basis matrix representation. Detailed derivations connect the energy functional, the Fock operator, excited determinants, and the interpretation of orbital energies. Restricted, unrestricted, and generalized formulations show how the choice of variational space affects spin symmetry, symmetry breaking, and the limitations of the Hartree--Fock approximation. The computational development covers orthogonalization, self-consistent-field iteration, convergence acceleration, overlap-based occupation selection, and orbital analysis, distinguishing orbital stationarity from stability. A connection to second-order M{\o}ller--Plesset perturbation theory explains the correlation-energy expression and the cost of transforming electron-repulsion integrals from atomic to molecular orbitals. The basis-set and integral development examines radial and angular flexibility, contraction, basis-set incompleteness, and superposition error. The Gaussian product theorem leads to one- and two-electron integrals, recurrence relations, integral screening, and low-rank representations. Worked examples and exercises with detailed solutions connect these derivations to practical calculations. Historical perspectives and explicit notation conventions provide context for the approximations and algorithms that underpin molecular electronic-structure theory.
Recently, we found a method to reconstruct the dilatation operator (sphere Hamiltonian) from a regulated conformal field theory groundstate. In this paper, we explore methods to construct the whole global conformal algebra, and test our construction using fuzzy sphere regularization. Starting from a groundstate of the same Hamiltonian, these methods perform better than constructions of the conformal generators based on a Hamiltonian density, are model-independent, require no additional tuning, and improve with system size. One purpose of reconstructing the conformal algebra is to identify conformal primary states, which we do with some success. We also find further evidence supporting the model of the short-distance corrections to the entanglement Hamiltonian proposed earlier and use it to make systematic improvements.
We propose a scheme to realize Weyl superfluidity from topologically trivial bands in the strongly correlated regime of a three-dimensional optical Raman lattice. The scheme builds on a pairing mechanism arising from the interplay between a large Zeeman splitting and strong Hubbard interaction. Spin-flip hopping suppressed by the large Zeeman detuning is resonantly restored when the attractive Hubbard interaction compensates the energy mismatch, yielding a correlated spin-orbit coupling that depends on the local particle configuration. Combining this density-dependent in-plane spin-orbit coupling with density-dependent spin-conserving interlayer tunneling extends the pairing mechanism to three dimensions. A self-consistent mean-field treatment of the microscopic model yields Weyl superfluids with two, four, or eight nodes, together with fully gapped weak topological superfluids. Tuning the interaction strength and particle filling drives transitions between these phases and controls the number of Weyl nodes. We further propose an experimental implementation with ultracold $^{40}\mathrm{K}$ atoms. Our results highlight density-assisted spin-orbit coupling as a mechanism for realizing Weyl superfluidity in strongly correlated systems.
The standard definition of entanglement entropy in quantum field theory requires regularizing the entangling surface and factorizing the Hilbert space, which in turn involves a choice of boundary conditions at the regularized surface. This raises two natural questions which are open at present. The first is under what conditions there is a choice of boundary conditions that leads to a unitary map between the original Hilbert space and the factorized one, which is a necessary condition for a well-defined entanglement entropy. The second concerns the situation where there are multiple such choices, in which case the question is whether they all yield the same entropy, or at least the same terms usually referred to as universal. Focusing on topological theories and using three-dimensional Chern-Simons theory as a concrete illustration, we show under specified assumptions that different such choices affect only the non-universal terms in the entropy, such that the remaining terms are universal in this sense as well, while we explicitly demonstrate that boundary conditions corresponding to non-unitary maps can change these terms. We then explain how a similar argument applies to two-dimensional conformal field theories and discuss a condition for universality in general theories.
We construct a universal quantum computational encoding via braiding in Links--Gould fusion spaces associated to $U_q^H(\mathfrak{sl}(2|1))$ where $q$ is on the unit circle and is not a root of unity. The construction uses only neglectons and is realized in the morphism spaces $\mathrm{Hom}_{U_q^H}(V(0,\alpha),V(0,-\frac{1}{2})^{\otimes 2N}\otimes V(0,\alpha)).$ Under explicit positivity and arithmetic constraints these spaces admit a $2^N$-dimensional computational subspace with a positive definite Hermitian form. We prove single-qubit density in $\mathrm{U}(2,1)$ and approximate arbitrary unitary operators on $N$-qubit computational subspaces with arbitrarily small leakage. The calculations use explicit inclusions, projections, and Hermitian pairings without requiring $F$-matrices.
The formalism of non-equilibrium dynamics for the dipole-symmetric $U(N)$ model involving $N$-component charged scalar fields is studied on the Schwinger-Keldysh contour by a systematic $1/N$ expansion of two-particle-irreducible (2PI) effective action to the next-to-leading order (NLO). The differential equations describing non-equilibrium evolution equations of two-point functions and field expectation values related to the symmetry breaking in the dynamics are derived, which encompass scatterings between modes essential in the late-time evolution and thermalization beyond the scope of the mean field. At the late-time regime of the evolution, the leading-order (LO) gradient expansion is performed to construct the vertex-resummed kinetic theory by encoding non-perturbative effects in the vertex through the resummation, which is distinct from the standard kinetic theory written by the weak-coupling expansion.
The predominantly $d_{x^2-y^2}$-wave pairing symmetry of cuprate superconductors is well established, yet its microscopic manifestation in local Cooper-pair tunneling remains less explored. Here, we investigate Bi$_{1.2}$Pb$_{0.8}$Sr$_2$CaCu$_2$O$_{8+\delta}$, using Josephson scanning tunneling spectroscopy with a conventional $s$-wave superconducting Pb tip. We observe a zero-bias conductance enhancement whose approximately quadratic dependence on junction conductance is consistent with phase-diffusive Josephson tunneling. Atomic-resolution conductance maps and site-resolved spectra reveal a pronounced intra-unit-cell modulation, with enhanced Josephson response near oxygen sites and strong suppression near copper sites and along diagonal directions. Microscopic calculations incorporating the bilayer electronic structure and realistic Wannier-based tunneling matrix elements reproduce the observed spatial pattern through interference between pairing contributions of opposite signs. Our results reveal how the sign-changing $d$-wave superconducting order parameter manifests itself in atomic-scale Josephson tunneling, providing complementary evidence for unconventional pairing symmetry in cuprates.
Nonreciprocal charge transport, where current flows preferentially in one direction, has become a key topic across quantum materials. This review covers some recent progress in bulk crystals, artificial heterostructures, van der Waals systems, high-temperature superconductors, and magnetic materials. The review discusses both intrinsic origins, such as band-structure effects, and extrinsic ones, including vortex motion, device geometry, and heating artifacts. A central focus is the superconducting diode effect due to its application potential, which shows different critical currents for opposite directions. The review also examines how symmetry breaking, spin-orbit coupling, and magnetic order contribute to the observed responses. However, there remain challenges when many exciting findings lack a unified picture, and the field continues to debate the relative importance of various mechanisms. The review highlights key open questions and suggests future directions, including better experimental standards and device integration. This review aims to give a balanced view of what is known, what is uncertain, and where the field might go next.
Quantum geometry, comprising the Berry curvature (BC) and the quantum metric (QM), underpins a wide array of topological and transport phenomena. However, in most solid-state platforms, BC and QM signals are inherently entangled, making their experimental separation highly challenging. Here, we demonstrate that the chiral limit of type-II semi-Dirac semimetals provides a symmetry-protected mechanism to cleanly isolate the QM. At the chiral limit where the spin-orbit gap $m_z=0$, chiral and $\mathcal{PT}$ symmetries strictly suppress the BC, its dipole (BCD), and the shift current, leaving the QM and its dipole (QMD) as the sole sources of the optical and nonlinear Hall responses. This pure-QM regime exhibits distinct experimental fingerprints, including a divergent longitudinal optical conductivity and a QMD-induced nonlinear Hall conductivity that exhibits a pronounced singularity as the chemical potential approaches the nodal point. Turning on a finite $m_z$ reactivates the BC channels, transitioning the system from a pure-QM phase into a mixed geometric phase. By deriving a scaling law for the nonlinear Hall conductivity, we establish a direct experimental strategy to separate the mixed Drude, BCD, and QMD contributions based on their distinct relaxation-time dependencies. Our findings identify chiral type-II semi-Dirac semimetals as highly tunable platforms for isolating and probing intrinsic quantum geometric effects.
Hecke operators can be used to relate characters of rational conformal field theories with different central charges, but it has remained a mystery how to interpret these relations physically. We offer a simple explanation in terms of self-duality under asymmetric orbifolds. Self-dual orbifolds also give more general identities beyond the familiar Harvey-Wu construction, which we illustrate through examples.
Quantum impurity calculations become challenging when multiple correlated orbitals are treated explicitly, particularly in nonequilibrium steady states. We introduce Coupled-Cluster Coupled Lindblad (C$^3$L), a deterministic approach that combines the recently developed coupled-Lindblad compact bath representation with coupled-cluster theory to compute steady states and Green's functions directly in imaginary and real frequency. C$^3$L has favorable polynomial computational complexity and avoids the sign problem of quantum Monte Carlo (QMC). In a real-time multiorbital benchmark, it agrees closely with state-of-the-art QMC while reducing computational cost by four to five orders of magnitude, with a further 10--100-fold speedup on a GPU. Beyond the practical reach of established real-time QMC solvers, four-orbital nonequilibrium impurities with general interactions and biased reservoirs become accessible with C$^3$L. We obtain resonance-resolved transport signatures relevant to scanning tunneling microscopy experiments on molecular junctions.
We study $S=1$ compass models on the square and kagome lattices with bond-dependent bilinear and biquadratic interactions parametrized by an angle $\theta$. For compatible geometries, we determine the exact ground-state manifolds throughout the interval $\pi/4\leq\theta\leq3\pi/4$. At each endpoint, a product of on-site unitaries maps the Hamiltonian to the Laplacian of a configuration graph $\mathcal{G}$ in the $S=1$ Cartesian basis. These endpoints are exact Rokhsar-Kivelson (RK) points, with one ground state per dynamically connected component of $\mathcal{G}$. Each such state is an equal-amplitude superposition in the transformed basis and acquires configuration-dependent phases upon transforming back to the original basis. Both models possess $m=O(L)$ independent and mutually commuting conserved $\mathbb{Z}_2$ line charges, where $L$ is the linear system size, forcing a ground-state degeneracy of at least $2^m$ at the RK endpoints. Throughout the interior region, $\pi/4<\theta<3\pi/4$, the ground-state manifold on each lattice is instead spanned by two product states, both annihilated by the Hamiltonian. On both lattices, each RK endpoint also hosts a first-order transition into this intervening interior phase spanned by the two product states with long-range order.
We construct an exact map between continuum fermion fields and lattice fields in 1+1 dimensions. This map rewrites a continuum Hamiltonian as a lattice Hamiltonian with nearest-neighbor couplings and an infinite-dimensional local Hilbert space. The resulting lattice model reproduces exactly the energy spectrum, global operator algebra, chiral symmetries, and anomalies of the continuum QFT on any finite lattice. Unlike domain wall fermions, truncating the local Hilbert space introduces no extra massless modes, and the entanglement entropy of an interval converges as the truncation is removed. The lattice local algebras are of type I and lie between the type III continuum algebras of nested spatial regions, in accordance with the split property. We demonstrate this construction explicitly for $N$ Majorana fermions, realizing the $\mathrm{O}(N)_\mathrm{L}\times\mathrm{O}(N)_\mathrm{R}$ lattice chiral symmetry. We also construct an exact lattice model for the Schwinger model and numerically reproduce the mass gap $e/\sqrt{\pi}$.