Papers

Conclusive identification of an altermagnetic state requires going beyond mere symmetry arguments. We illustrate this in a combined computational and experimental study of the rutile-like material CuF$_2$, which is on the list of predicted altermagnets. Using ab initio and linear spin-wave calculations supplied by magnetization measurements, we show that CuF$_2$ in its experimental monoclinic structure can be described by a spin-$\frac12$ model of weakly coupled square-lattice layers with the in-plane coupling $J_1\simeq 115$ K and two synergistic antiferromagnetic interplane couplings amounting to 4% and 8% of $J_1$, respectively. Driven by long-range superexchange, these interlayer couplings are oblique to the square planes, resulting in the unit-cell doubling in the magnetically ordered state, thus effectively suppressing any altermagnetic band splitting. Concurrently, we identify unusually strong Dzyaloshinskii-Moriya interactions, $|\mathbf D|/J_1\simeq 0.3$, that produce spin canting and, together with order-by-disorder effect, pin the Néel vector to the crystallographic $b$-axis. Additionally, DM anisotropy promotes magnon band splitting, but these bands remain non-chiral. Our results highlight the importance of relativistic effects even in $3d$ magnets with altermagnetic symmetries.

YRu$_3$Si$_2$ and LaRu$_3$Si$_2$ host the highest charge density wave (CDW) transition temperatures ever reported in kagome metals, $T_{\mathrm{CDW}}\approx 800$ and 400~K, with propagation vectors $Q_{\mathrm{CDW}}\approx(1/2,0,0)$ and $(1/4,0,0)$, respectively. The microscopic mechanism behind these record values has remained unresolved. Here, we combine anharmonic phonon renormalization extracted from molecular dynamics driven by a machine-learned force field with mode-resolved electron-phonon coupling (EPC) analysis to identify this mechanism. The CDW is driven by mode-selective EPC: the Ru out-of-plane phonon modes couple the Ru-$d_{xz}/d_{yz}$ and Si-$p_x/p_y$ orbitals, and the phonon linewidth peaks sharply at $Q_{\mathrm{CDW}}$, while the featureless electronic susceptibility rules out Fermi-surface nesting. Phonon anharmonicity melts the CDW, and the anharmonic phonon spectra reproduce both $Q_{\mathrm{CDW}}$ and $T_{\mathrm{CDW}}$ in good agreement with experiments. Molecular dynamics simulations also visualize the CDW melting in real space. Chemical bonding analysis further shows that the smaller Y$^{3+}$ radius strengthens the Ru-Ru bonds, enhancing lattice rigidity and accounting for the factor-of-two higher $T_{\mathrm{CDW}}$ of YRu$_3$Si$_2$. Our results establish a unified microscopic picture of CDW formation and melting in kagome metals YRu$_3$Si$_2$ and LaRu$_3$Si$_2$.

We study dielectric properties of holographic insulators from the quantum geometry of the ground state. We realize the insulating state by the pseudoscalar interaction of holographic fermions and calculate the fermionic Green function to extract the effective hamiltonian. We then derive the quantum metric and Berry curvature to compute the transports and finally get the dielectric constant from the imaginary part of conductivity.

Multipolar-fluctuation analysis based on density functional theory combined with dynamical mean-field theory is extended from $4f^1$- to $4f^2$-electron systems. Two methodological developments are presented. First, many-particle states are constructed within the $j$-$j$ coupling scheme in the $j=5/2$ subspace, so as to reproduce the crystalline-electric-field splitting of the $4f^2$ Hund's-rule ground-state multiplet. Second, multipolar susceptibilities and interactions between $4f^2$ multiplets are derived through a mapping from single-particle to many-particle bases. We apply this framework to PrCdNi$_4$, which has a non-Kramers $\Gamma_3$ doublet ground state, and propose a $(3z^2-r^2)$-type antiferroquadrupolar order at $\boldsymbol{q}=(2\pi,\pi,0)$ driven by the competition between nearest- and fourth-nearest-neighbor interactions. The formalism developed here is applicable to general $4f^n$-electron systems.

Superradiant phase transitions are fundamental phenomena in light-matter coupled systems. Here, we uncover a novel class of superradiant criticality that is topologically distinct from previously known superradiant transitions. Using cavity-mediated cluster-Ising chains as an illustrative example, we numerically demonstrate that the critical line separating the superradiant phase from the cavity topological phase hosts robust symmetry-protected edge degeneracies, a feature absent in conventional superradiant transitions. Remarkably, although its local bulk critical properties are indistinguishable from those of the previously identified topologically trivial superradiant transition, the two criticalities cannot be smoothly connected without breaking the protecting symmetries or passing through a multicritical point. We further show that such topological superradiant criticality is generic, also occurring in cavity-mediated $\mathbb{Z}_{n}^{}$ cluster-qudit chains, as supported by complementary lattice simulations.

Conventional understanding of iron-based superconductivity is usually established based on electronic bands at the Fermi level, leaving deeper bands overlooked as potential factor. Here, we expand this view by demonstrating that a deep-lying dz2 band below the Fermi level can be employed to enhance the superconducting paring strength. By using scanning tunneling microscope to mechanically change the crystal lattice of an iron-based superconductor, we observe an upward shift of the deep-lying dz2 band related feature, leading to hybridization with the primary superconducting bands at the Fermi level. We visualize the novel evidence of this band hybridization and resulting enhanced superconducting gap through quasiparticle interference imaging, providing conclusive evidence that engineering such correlations between deep and pairing-active bands is a potent mechanism for amplifying the superconducting gap. This work refines the conventional view of pairing-relevant electronic structures and establishes band hybridization as an effective way to optimize superconducting materials.

We investigate fermionic spectral functions in a two-current Gubser-Rocha background with linear-axion momentum relaxation. Serving as a comparison channel, the dipole coupling $p_1$ is found to produce a soft asymmetric reconstruction without opening a clean hard Mott gap. Our main analysis then focuses on two axion-dependent non-minimal couplings modulated by current mixing. The $p_2$ tensor channel suppresses the zero-energy Fermi peak and shifts the dominant spectral weight to finite frequencies, resulting in a flat-bottom reconstruction. In contrast, the $p_3$ vector channel creates a strong spectral asymmetry in momentum space, generating open, Fermi-arc-like segments. Varying the momentum-relaxation strength $\beta/\mu$ and the doping parameter $\chi$ reveals a channel-dependent response to the two-current background. Increasing $\beta/\mu$ generally broadens the $p_2$ response, whereas the one-sided $p_3$ feature varies non-monotonically under changes of the background parameters. These results clarify how current mixing, axion-induced momentum relaxation, and non-minimal fermion couplings jointly reshape holographic fermionic excitations. These results clarify how current mixing, axion-induced momentum relaxation, and non-minimal fermion couplings jointly reshape holographic fermionic excitations.

Two dimensional Janus semiconductors integrating spin-valley coupling, piezoelectricity, and tunable optical responses offer a platform for multifunctional nanodevices. Here, first-principles calculations reveal complementary composition and strain effects in CrSiCN4 and CrGeCN4 monolayers. Both are found to be nonmagnetic direct-gap semiconductors, with gaps of 1.23 and 1.09 eV using the Perdew-Burke-Ernzerhof functional including spin-orbit coupling, respectively. HSE06 hybrid-functional calculations retain the direct-gap character, yielding gaps of 1.46 eV for CrSiCN4 and 1.19 eV for CrGeCN4. Opposite out-of-plane spin character and Berry curvature emerge at K and K'. Biaxial strain reduces the respective gaps from 1.59 to 0.86 eV and 1.44 to 0.63 eV, drives direct-to-indirect transitions, and redshifts absorption while preserving valley spin contrast. CrGeCN4 exhibits larger in-plane piezoelectric response, whereas CrSiCN4 exhibits larger out-of-plane magnitude. Band-edge alignment satisfies the oxygen evolution reaction requirement but provides insufficient driving force for the hydrogen evolution reaction, motivating further strain-induced band-edge modulation toward overall water splitting. These results establish composition and strain as complementary controls for tailoring Cr-based Janus monolayers for valleytronic, optoelectronic, electromechanical, and photocatalytic applications.

Conditional mutual information (CMI) probes spatial non-Markovianity and plays a central role in a recently developed framework for defining mixed-state phases based on local reversibility. This framework sharply distinguishes exponentially decaying from algebraically decaying CMI, since the latter obstructs equivalence to a state with finite Markov length. Here we show that states that flow to the same renormalization-group (RG) fixed point can nevertheless exhibit qualitatively different CMI. Starting from a critical Gibbs state of a finite-range local classical Hamiltonian, whose CMI vanishes beyond the interaction range, we show that an RG-irrelevant perturbation that breaks detailed balance generically generates algebraically decaying CMI. Crucially, these power-law tails are cutoff-suppressed: although they lead to an infinite Markov length at every fixed lattice cutoff, they vanish as a positive power of the cutoff in the continuum limit. We construct solvable models that exhibit this phenomenon and predict that the Ising-symmetric critical point of Toom's cellular automata generically exhibits such behavior. We also find analogous cutoff-suppressed CMI in the high-temperature paramagnetic phase of the long-range Ising paramagnet, in contrast with the genuine power-law CMI at the finite-temperature critical point in this same model that survives the continuum limit. We also derive a general result that in one spatial dimension, CMI decays faster than the inverse square of the buffer length if and only if the long-distance physics is Markovian.

We study a hybrid system of coupled cavities, with or without two-level atoms doped inside. By employing a building-block construction facilitated by nonlinear Stark coupling, we identify a manifold of exact many-body eigenstates that remain analytically tractable across arbitrary lattice geometries and atom distributions. We demonstrate that these exact states exhibit a dual physical nature depending on their spectral positioning: when embedded within the chaotic many-body spectrum, they manifest as quantum scars that violate the eigenstate thermalization hypothesis and undergo weak ergodicity breaking; conversely, as ground states within fixed-total-excitation sectors, they exhibit off-diagonal long-range order and form polariton condensates. Furthermore, numerical calculations of local excitation-number fluctuations suggest that negative Stark coupling shifts the Mott-insulator to superfluid transition toward weaker inter-cavity hopping. Our findings provide a versatile framework for engineering both coherent quantum phases and non-thermalizing states in diverse light-matter architectures.

Emergent phenomena in quantum materials arise from interactions among different degrees of freedom. Identifying these interactions and establishing their roles in ordered states are central problems in condensed-matter physics and provide a basis for controlling material properties. Many relevant low-energy excitations and gaps lie in the terahertz (THz) and mid-infrared (MIR) range, where intense phase-stable fields can both interrogate nonlinear dynamics and drive selected degrees of freedom far from equilibrium. This review surveys recent progress in probing and manipulating quantum materials with strong-field THz and MIR radiation, with emphasis on nonlinear electronic dynamics, collective-mode coupling, symmetry-sensitive responses and field-induced changes in electronic structure and ordered states. Particular attention is given to developments enabled by the Synergetic Extreme Condition User Facility (SECUF).

Finite photon momentum allows second-order photocurrents in centrosymmetric space groups, where the conventional bulk photovoltaic effect is forbidden. Here we study the photon-drag response of altermagnets and show that its angular dependence reveals both the symmetry of the magnetic order and the Néel domain of the sample. For example, when a crystal rotation exchanges the two domains, the domain-even and domain-odd parts of the current appear in different angular harmonics, $4n$ and $4n+2$ for tetragonal $d$-wave altermagnets, so that two measurements rotated by $90^\circ$ on a single domain isolate the domain-odd current. We also find that these microscopic contributions exhibit opposite domain parities depending on light polarization. Under linear light, only the shift term is domain odd, while under circular light, the domain-odd channel switches to the injection, Fermi-surface, and contact principal-value terms. Mirror symmetries fix the angular phase of each harmonic and distinguish $d_{x^2-y^2}$, $d_{xy}$, and $g$-wave order. In contrast, conventional collinear antiferromagnets show no domain-odd photon-drag current, and in tetragonal ferromagnets the two parts share the same harmonics. Although the altermagnetic spin splitting does not require spin-orbit coupling (SOC), SOC is essential to observe the domain-odd charge current. Our work uncovers distinct signatures of altermagnetism in photon drag and provides a route to all optical magnetic readouts of altermagnets.

In the BCS theory of superconductivity the amplitude (Higgs) mode is degenerate with the pair-breaking threshold: its frequency coincides with $2\Delta$, so it is an edge singularity rather than a true collective mode. This is why after a sudden weak perturbation at $t=0$ its oscillations decay algebraically as $1/\sqrt{t}$. We show that the retardation effects due to the phonon dynamics in the strong-coupling theory lift this degeneracy. The Higgs mode detaches from the pair-breaking edge $2\Delta_g$, set by the spectral gap, and becomes a sharp subgap excitation. We determine its frequency from the longitudinal pair susceptibility evaluated directly on the real frequency axis, using the Eilenberger equations for Migdal–Eliashberg theory with the Einstein phonon spectrum. The response of the mass renormalization supplies at least two fifths of the displacement, and possibly all of it: with it switched off, the binding falls below the resolution of the calculation. Its consequences, however, are significant because a percent-level shift transfers about a quarter of the spectral weight of the amplitude channel out of the two-quasiparticle continuum into a discrete energy level. What experiment sees is therefore not the displacement itself but its consequence: amplitude oscillations that persist instead of decaying as $1/\sqrt{t}$.

We develop a constructive framework for characterizing modulated symmetries and their gauging in $d$-dimensional lattice systems. The modulation profiles are organized as a finite-dimensional representation of the space group acting on a finite Abelian internal symmetry group. Since the corresponding automorphism group is finite, the nontrivial spatial action factors through a finite quotient of the space group, leading to periodic modulation patterns and providing a classification framework for discrete Abelian modulated symmetries. The symmetry-allowed local interactions are systematically obtained from a kernel construction, which also yields an algebra of open operators. Upon gauging, its elements are transmuted into extended Wilson and boundary operators while retaining their algebraic relations. In the deconfined regime, the resulting algebra realizes a mixed 't Hooft anomaly, providing a microscopic route to Abelian crystalline symmetry-enriched topological phases (SETs). These SETs do not mix electric and magnetic sectors, which transform in mutually contragredient representations, thereby preserving their braiding pairing. We illustrate the framework through explicit examples and show that several models present in the literature fit naturally within our construction.

A long-term goal of quantum simulation is to faithfully reproduce the low-energy Hamiltonians of correlated quantum materials, establishing a direct connection between solid-state experiment, electronic-structure theory, and programmable many-body systems. Here, we introduce an integrated quantum-simulation architecture based on fermionic alkaline-earth atoms that enables programmable control over the key ingredients of multi-orbital material Hamiltonians. Long-lived clock states encode synthetic orbitals, their differential polarizabilities generate orbital-selective tunneling, and contact interactions provide multi-orbital Hubbard and Hund couplings. Spatially structured coherent driving on the ultra-narrow clock transition further realizes symmetry-selective inter-orbital hybridization, while the clock detuning independently controls orbital energy offsets. In this way, the spatial symmetries of solid-state orbitals can be encoded directly into the effective Hamiltonian, even though the atoms themselves remain in conventional $s$-wave Wannier orbitals of the lowest optical-lattice bands. We demonstrate the resulting integrated control using the four-band low-energy Hamiltonian of the bilayer nickelate La$_3$Ni$_2$O$_7$ as a demanding benchmark. Self-consistent calculations show that the microscopic parameters obtained from first-principles modeling can be reproduced within a single experimentally accessible lattice configuration and independently programmed over substantial parameter ranges. Our results establish a general route for translating material-derived multi-orbital Hamiltonians into programmable ultracold-atom quantum simulators.

Recent scanning tunneling microscopy has directly imaged electronic crystals in rhombohedral hexalayer graphene, and magnetotransport measurements suggest that superconductivity and charge-density-wave order emerge from a common spin-valley-polarized ferromagnetic metal at nearby carrier densities. Motivated by these observations, we ask whether collective modes in a magnetic Wigner crystal can mediate pairing in this setting. We address this question by studying the Cooper problem for two electrons in the first conduction band of the Wigner crystal. Unlike conventional phonon-mediated pairing, the collective mode (boson) energies and single-particle (fermion) dispersion are comparable scales controlled by the electron density, leaving no small parameter for an adiabatic expansion. Moreover, because the magnetic Wigner crystal is not time-reversal invariant, the usual Cooper logarithmic divergence in the pairing susceptibility is absent, so the attraction must exceed a finite threshold for pairing to occur. These unusual features motivate a numerical experiment to see whether the crystal's own vibrations can bind electrons. We obtain the crystalline ground state and its collective mode spectrum within Hartree–Fock and time-dependent Hartree–Fock approximation, and derive the electron–phonon Hamiltonian using the quasiboson approximation. Solving the resulting two-electron problem, we find that phonon-mediated attraction exceeds the pairing threshold, with chiral $p$-wave pairing as the leading instability. Within these approximations, we show that collective modes of a Wigner crystal can indeed favor chiral pairing despite broken time-reversal symmetry. Our results provide an encouraging starting point for developing a full many-body theory to study electronic crystallization and superconductivity.

Moiré materials host integer and fractional Chern insulators (FCIs) where time-reversal is broken spontaneously by flat band ferromagnetism. In twisted MoTe2, unlike in quantum Hall, opposite spins carry opposite Chern numbers and realize Ising ferromagnetism with gapped magnon excitations. Clarifying the nature of these collective modes and the origin of the magnon gap is key to understanding the stability of the Chern magnets in these materials. To do so, we develop a generalized single-mode approximation, which we call the symmetric mode ansatz (SyMA), to describe the low-energy magnon spectrum. We find it to be in exceptional agreement with numerical calculations at integer filling, and qualitatively accurate across fractional fillings including FCIs. To explain the accuracy of the SyMA, we present two families of Hubbard models (including the Haldane model and continuum ideal bands) whose collective modes are analytically solvable and for which the SyMA is either exact or an accurate approximation. For a class of these models where SyMA is exact, we prove two-sided bounds on the zero-momentum magnon gap in terms of the Chern number, Berry curvature, and quantum metric, revealing that uniform quantum geometry is sufficient for stabilizing magnetism in Chern bands.

We investigate how spontaneous symmetry breaking and symmetry-protected topology compete and cooperate in one-dimensional quantum spin-1/2 systems. We introduce two families of local Hamiltonians with $\mathbb{Z}^{\,}_{2}\times\mathbb{Z}^{\,}_{2}\times\mathbb{Z}^{T}_{2}$ symmetry which host a zoo of broken-symmetry phases with and without gapless boundary spins, namely, six long-range-ordered gapped phases that differ by their $\mathbb{Z}^{\,}_{2}$-symmetry-breaking patterns (FM$^{\,}_{x,y,z}$ and Neel$^{\,}_{x,y,z}$), their partner symmetry-protected topological phases (FM$^{\mathrm{SPT}}_{x,y}$ and Neel$^{\mathrm{SPT}}_{x,y}$), and two gapless phases (gFM$^{\,}_{z}$ and gNeel$^{\,}_{z}$) with incommensurate $\mathbb{Z}^{T}_{2}$-breaking magnetic long-range order and central charge $\mathsf{c}=1$. Direct transitions between competing gapped phases can be continuous or weakly first order. We demonstrate that continuous phase transition lines have exotic critical properties. For example, a line of deconfined quantum critical points (between the Neel$^{\,}_{x}$ and Neel$^{\,}_{y}$ phases) described by Tomonaga-Luttinger liquid theory is terminated by the gFM$^{\,}_{z}$ phase at a Lifshitz tricritical point which exhibits spontaneous breaking of the continuous U(1) symmetry despite the locality and one-dimensionality of the Hamiltonian, contrary to a naive expectation from the Hohenberg-Mermin-Wagner-Coleman theorem. Furthermore, critical lines between symmetry-protected topological phases with different $\mathbb{Z}^{\,}_{2}$-symmetry breaking (e.g., Neel$^{\mathrm{SPT}}_{x}$ and Neel$^{\mathrm{SPT}}_{y}$) additionally retain low-energy boundary degrees of freedom, realizing symmetry-enriched criticality (or a gapless SPT phase). Our results reveal unconventional mechanisms by which competing symmetry breaking and topology generate ordered critical phases and multicriticality.

We study symmetric gapped ground states of one-dimensional spin $S$ chains with a continuous exponential symmetry $U(1)\rtimes\mathbb Z_2$ with integer base $q$, where the U(1) charge has a modulated unit of charge $q^{L-j}$ decaying exponentially with site $j$. The simplest model is a quantum breakdown model that can be viewed as a $q$-deformation of the XXZ Haldane spin chain. We show that the topology of their symmetric ground states crucially depends on $S$ and $q$. For integer $S$, odd $q$ allows a nontrivial $\mathbb Z_2$ Haldane-type symmetry-protected topological (SPT) phase with protected edge modes, while even $q$ allows no nontrivial SPT phase. For half-odd integer $S$, odd $q$ prohibits any unique symmetric gapped ground state due to a Lieb-Schultz-Mattis obstruction, whereas even $q$ enforces a novel symmetric gapped phase which we name as the “half-SPT" phase. Unconventionally, the half-SPT phase only has a symmetry protected edge mode on one edge, and has half of the string orders of an SPT phase. Our results uncover a new type of symmetry-protected gapped phases beyond existing classification schemes.

Superconductivity and intrinsic topological order can intertwine in ways that go beyond simple coexistence. Here we develop a classification framework for (2+1)D gapped superconductors with condensate charge $2ne$. By focusing on the topological properties of superconducting vortices, we precisely characterize this interplay. We obtain a classification with increasing levels of intertwinement, from the well known invertible superconductors without topological order, to untwisted and twisted SC$^\ast$, and finally to SC$^{\sharp}$. Our main finding is the family SC$^{\sharp}$, in which the elementary vortex carrying $h/(2ne)$ flux cannot be factorized into an invertible superconductor vortex dressed by bulk anyons, and every elementary vortex is necessarily non-Abelian. For such phases, we also obtain no-go results: the elementary vortex sector has quantum dimension at least $\sqrt{6}$ and cannot satisfy Fibonacci fusion rules. We develop a systematic algebraic framework to obtain all these superconducting phases through anyon condensation, allowing us to construct several infinite families of examples and make connections to anyon superconductivity. Finally, we introduce primitive SC$^\sharp$ phases for which factorization of every nontrivial vortex sector is obstructed, and argue that they cannot arise by disordering the relative phases of lower-charge superconducting condensates. Our classification scheme based on vortex properties allows us to uncover new distinctions between topologically ordered superconductors and constrain how they can be realized.

Topologically ordered superfluids (TOSFs) support deconfined, gapped anyonic excitations while remaining gapless because of Goldstone modes. We develop a general framework for characterizing their topological data in $(2+1)$-dimensional bosonic systems with spontaneously broken charge ${\rm U}(1)_{\rm c}$ symmetry. Gauging ${\rm U}(1)_{\rm c}$ maps a TOSF to a gapped topological order enriched by a dual ${\rm U}(1)_{\rm dual}$ symmetry with vanishing Hall conductance, while gauging ${\rm U}(1)_{\rm dual}$ recovers the TOSF. This two-way mapping allows the topological data of the TOSF, including the condensate charge, deconfined anyon content, and topological properties of vortices, to be systematically encoded using the algebraic framework of symmetry-enriched topological orders. In particular, superfluid vortices share the topological properties of flux defects associated with the residual discrete symmetry in the gapped anyon sector. We develop complementary algebraic and field-theoretic formulations of this framework, with the latter also suggesting a natural transition to a gapped topologically ordered phase. Additionally, using parton constructions, we present examples of TOSFs with non-Abelian vortices in bosonic systems.

In this work we study phenomenological Landau theories of non-relativistic magnetic systems, generalizing work on the collinear case to coplanar and non-coplanar orders. Focusing on zero-wavevector ($\boldsymbol{k}=0$) magnetic orders described by a single irreducible representation of the crystallographic point group, we construct the symmetry-allowed free energies to quartic order for all possible multi-dimensional irreducible ordering channels. We find distinct Landau theories for tetragonal, trigonal/hexagonal, and cubic symmetry. Similar to the case of spin-nematic fluids, we find two natural outcomes: a collapse to a lower-symmetry collinear phase or a genuinely coplanar or non-coplanar order where the order parameters form a mutually orthogonal set in spin space – reminiscent of the $A$ and $B$ phases in ${}^3$He. We show in general that this symmetry-broken phase realizes the spin space group associated with the spatial representation of the order parameter sharing the same parent space group as the paramagnetic phase. This provides a direct link between the Landau and spin space group approaches. We calculate key observables using this Landau approach, including net magnetization, spin conductivity, multipolar moments, and piezomagnetism, connecting our results to constraints from the underlying spin space group. Examples of coplanar and non-coplanar magnetic orders for each case are worked out in detail. Finally, we discuss the relationship of the lower-symmetry collinear phases to the usual collinear spin groups, as well as connections to atomic altermagnetism, superfluid ${}^3$He and electronic nematic phases.

Finding excited states and excitation gaps in frustrated spin systems using Variational Quantum Eigensolvers (VQE) is complicated by state-ordering inversions. In the frustrated spin-1/2 $J_1$-$J_2$ Heisenberg model, standard single-sector algorithms like Variational Quantum Deflation (VQD) in $S_z=0$ fail when $J_2/J_1 < 0.25$. In this regime, the lowest-lying excitation in $S_z=0$ is a Triplet ($S=1$), which lies below the Excited Singlet ($S=0$). Standard deflation projects out the ground singlet and converges onto the Triplet state, misidentifying it as the Excited Singlet. Here, this work presents a Dual Spin-Sector VQE framework that resolves these state-ordering inversions applied to frustrated $J_1-J_2$ models on 1D spin chains and 2D rectangular lattices. Firstly, by optimizing the ground Triplet state in the $S_z=1$ sector (where singlet states cannot exist), mapping it into $S_z=0$ via the total spin-lowering operator $S^- = \sum_i S_i^-$, and evaluating a dual-sector penalty cost function, the Excited Singlet ($E_S$) is isolated without variational ambiguity. Numerical state-vector simulations confirm exact convergence to machine precision with unit overlap fidelity. The method captures key physical features, including the gapless phase, the gapless-gapped critical point at $J_2/J_1 \approx 0.2411$, the Majumdar-Ghosh dimer point ($J_2/J_1 = 0.50$), and the 2D non-magnetic frustrated regime ($J_2/J_1 \approx 0.40 - 0.60$). Finite-shot sampling simulations and gate-scaling analytics up to $N=100$ qubits demonstrate the resource efficiency and shot resilience of the algorithm for near-term quantum execution.

The magnetic order of a material is usually predicted by comparing the energies of trial spin configurations, a strategy that cannot reach orders outside the chosen set and rapidly becomes intractable as the number of magnetic sites grows. We show that the order can instead be identified directly from the paramagnetic state: the leading eigenmodes of its self-consistent magnetization response, obtained with spin–orbit coupling at arbitrary wavevector within the primitive cell, determine both the ordering wavevector and the pattern of moments, with no candidate configurations. With no prior assumption about the order, the method correctly reproduces the G-type stacking with out-of-plane moments in the altermagnet candidate KV$_2$Se$_2$O, the $3{:}1$ ferrimagnetic tetrahedra of Cu$_2$OSeO$_3$, and the incommensurate spiral instability of monolayer NiI$_2$. Our results establish the response of the paramagnetic state as a predictive and unbiased route to assessing magnetic order, enabling systematic searches for complex magnets.

A major application of analog quantum hardware is quantum simulation, where a system evolves over time according to a given Hamiltonian. One challenge when implementing the Hamiltonian on a programmable quantum simulator is the availability of distinct coupling types, many of which go beyond the conventional ZZ-couplings found in Ising Hamiltonians that are naturally implemented by various platforms. In prior work, we have developed a method based on domain wall encoding to simulate one-dimensional spin chains using only Ising Hamiltonians, which would otherwise require XX+YY-couplings as well. Here, we implement the method on a commercially accessible Rydberg atom quantum device, and simulate the time evolution of the Heisenberg XXZ model with various anisotropies. We successfully probe the XY and Ising phases of the model and reproduce the qualitative behavior of several one- and two-body observables in both phases, as well as at the critical point. Our work augments the toolbox to simulate canonical quantum many-body systems on analog quantum simulators.

Spatially varying lattice distortions can produce local changes in electronic properties that are obscured by measurements averaging over extended regions. With its atomic-scale spatial resolution, scanning tunneling microscopy (STM) provides, in principle, a means of quantifying such distortions locally. A widely used approach for extracting local strain from STM images is the Lawler–Fujita (LF) algorithm [Lawler et al., Nature 466, 347 (2010)], which determines the displacement field from the phase of the lattice modulation and subsequently obtains the strain by differentiation. However, this approach requires two-dimensional phase unwrapping, which can fail in regions where the phase is ill-defined, particularly near topological defects such as edge dislocations. Here, we introduce an alternative approach that circumvents these limitations by directly measuring the local wave vector in real space. We derive the relationship between the local wave vector, strain, and the phase gradient, and show that the local wave vector mapping (LWM) algorithm remains robust even when the phase itself is ill-defined. This makes the method particularly well suited for imaging the phase-gradient textures associated with vortices and other topological defects. We benchmark the algorithm using simulated data containing known lattice distortions and artificially generated vortices. Finally, we apply the method to experimental STM data and resolve the charge density wave (CDW) incommensurabilities, lattice distortions, and CDW phase vortices in 4Ha-NbSe2 and 2H-NbSe2. The physical implications of these observations were recently reported by S. Sajan, X. Yang, et al. [arXiv:2607.20335 (2026)]. The program package and the example usage is publicly available at the GitHub: https://github.com/jsntxyang/LocalWavevectorMeasuremnt.

Optically exciting a typical low-dimensional semiconductor produces a nodeless \(s\)-type exciton as its lowest-energy bound state. Here, we explain how Coulomb phase matching stabilises a quantum-vortex exciton as the lowest bound state in flat Chern bands. Using a prototypical Yin–Yang kagome lattice, we demonstrate that increasing the spin–orbit coupling drives a transition of the lowest exciton from a quantum-vortex state to a zero-winding state, while leaving the band Chern numbers unchanged. We trace this behaviour to a gauge-invariant combination of exciton phase differences and Bloch-overlap phases that can reduce the Coulomb energy. By comparing states with identical wavefunction amplitudes, we isolate this phase contribution and show that it is sufficient to drive the reversal in exciton ordering. We classify exciton topology by the momentum-space wavefunction winding relative to the conduction–valence Chern-number difference,connecting the competing states to circular-polarisation selection rules. We then show that the resulting reordering can be tracked directly in the optical absorption spectrum, through the transition from a dark vortex exciton to a bright zero-winding exciton. These findings establish a microscopic link between exciton topology, Coulomb binding, and optical response that extends beyond the information contained in the underlying electronic band Chern numbers.

We construct unitary, local, 3+1-dimensional conformal field theories with finitely many fields whose thermal state breaks a continuous global symmetry at every temperature. They are finite-$N$ versions of the Chaudhuri–Choi–Rabinovici theories, whose planar circle of fixed points has an ordered arc. The circle is lifted at order $1/N^2$, and an infinite family of fixed points on this arc reaches arbitrarily weak coupling, where the superfluid is under parametric control. We also show that weakly gauging the symmetry gives a superconductor over an exponential range of temperatures.

Understanding the non-equilibrium dynamics of quantum many-body systems plays a central role in modern many-body physics. Intriguing insights emerge from investigating how quantum resources, which are essential for achieving unambiguous quantumness, are generated and spread under chaotic quantum dynamics. In fermionic systems, non-Gaussianity constitutes an important resource beyond entanglement, characterizing the deviation of generic quantum states from free-fermion states. In this Letter, we propose using the replica twist entropy, defined through the expectation value of a replica rotation operator with a tunable angle $\alpha$, as a natural probe of non-Gaussianity in pure fermionic states. After deriving its behavior for typical many-body states, we establish a general framework for analyzing the replica twist entropy in solvable Sachdev-Ye-Kitaev models in the large-$N$ limit. Applying this framework to the dynamics of the thermofield double state, we uncover a novel dynamical phase diagram in the parameter space of $\alpha$ and evolution time $t$, exhibiting spontaneous $Z_2$ symmetry breaking at $\alpha=\pi/4$ and universal cusps as a function of $\alpha$ in the long-time regime. Our results pave the way for studying non-Gaussianity in strongly correlated fermionic systems and reveal a new class of dynamical transitions probed by non-Gaussianity.

Hybrid metal-semiconductor quantum circuits offer a controlled setting for realizing and probing strongly correlated quantum matter. A largely open question that may be addressed by such simulators is whether coupled critical states can combine into new non-Fermi liquid (NFL) phases. Inspired by the recent realization of a two-site charge-Kondo circuit [W. Pouse et al., \href{https://www.nature.com/articles/s41567-022-01905-4}{Nat. Phys. 19, 492 (2023)}], we uncover the fate of coupled Kondo anyons emerging from the two-channel-Kondo critical point at each site. Bosonization and quantum Brownian motion methods yield the full quasiballistic phase diagram and low-temperature transport properties, while numerical renormalization group calculations resolve the complementary weak-coupling limit. Together, these provide a unified description, and reveal robust NFL phases with continuously tunable transport and susceptibility exponents. Stronger inter-site coupling ultimately produces a screened Fermi liquid.