Papers

We present a numerical study of a blockade Hamiltonian with a local $\mathbb{Z}_2$ symmetry. For such models, the existence of a topologically ordered ground state has been proven rigorously for weak Rabi driving [T. F. Maier et al., PRX Quantum 6, 030340 (2025)]. However, the phase diagram beyond weak driving is still an open question. We perform large-scale infinite-size density matrix renormalization group (iDMRG) simulations on a cylinder and map out the full phase diagram of the model. We find a single continuous phase transition between the topologically ordered phase and a trivial paramagnetic phase, and confirm numerically the stability of the topologically ordered phase up to Rabi drives comparable to the characteristic energy scale of the system. Furthermore, we compute the excitation gaps and show that the charge gap remains open across the phase transition and charges become confined in the trivial phase. On the other hand, the gap in the symmetric sector closes at the transition, consistent with the condensation of flux excitations.

In this work, we investigate a continuum model of two-dimensional electrons interacting via long-range Coulomb forces and subject to a triangular periodic potential at filling factor $\nu=2$. Using neural quantum states based on message-passing neural networks optimized with variational Monte Carlo, we determine the ground-state phase diagram as a function of periodic potential strength and Zeeman field. Although the noninteracting system is expected to form a conventional band insulator, we show that strong correlations can qualitatively reshape the insulating state and, in part of the phase diagram, suppress the band insulator in favor of a correlated metallic phase, with a first-order transition separating the two regimes. Moreover, the metal–insulator transition exhibits a strong dependence on spin polarization: the unpolarized system becomes insulating at substantially weaker periodic potentials through the formation of an $s$-wave molecular insulator, where opposite-spin electrons bind near each potential minimum, whereas the fully polarized system requires a significantly deeper potential and instead forms a symmetry-broken orbital nematic molecular crystal. This spin-dependent molecular transition gives rise to discontinuous magnetization curves, metamagnetic transitions, and several multicritical points in the phase diagram, together with clear signatures in the density profiles, real-space correlation functions, and structure factors. To further elucidate the role of the long-range character of the Coulomb interaction, we also study short-range repulsive interactions, which can be realized with ultracold-atom platforms. We find that the qualitative structure of the many-body phase diagram remains unchanged, demonstrating the robustness of our results across different interaction models.

In conventional Landau theory, simultaneous continuous onset of superconductivity and the breaking of additional symmetries generally requires a multidimensional order parameter or fine tuning. We show that symmetry fractionalization provides a different route. In a Kondo lattice with a $\mathbb Z_2$ spin liquid, the Kondo fields inherit the projective symmetry action of the spinons. When the projective time-reversal action on these fields squares to $-1$, the projective symmetry algebra forbids a condensate that preserves time-reversal symmetry and enforces twofold degeneracy of the critical modes. Because Kondo condensation in a $\mathbb Z_2$ spin liquid also breaks electromagnetic $U(1)$ symmetry, superconductivity and time-reversal symmetry breaking can emerge at a single continuous transition, even if crystal symmetry admits only one-dimensional irreducible representations. We demonstrate this mechanism in an anisotropic Kondo-Kitaev model, where superconductivity and the breaking of time-reversal and mirror symmetries emerge simultaneously.

We construct and classify $Z_2$ quantum spin liquids (QSLs) of fermionic partons on the dipolar-octupolar (DO) pyrochlore lattice. The DO pseudospin shares the space-group and time-reversal algebra of the effective spin-1/2 Kramers doublet, its projective symmetry group (PSG) yields the same 48 symmetric $Z_2$ classes as the generic fermionic classification. We show, the distinct DO symmetry action, encoded in a set of sublattice-independent operators, selects a physically different set of symmetry-allowed mean-field channels, so that the resulting ansatze, spinon spectra, and observables differ from both the effective spin-1/2 case and the bosonic DO classification. Decomposing the anisotropic XYZ exchange model into all symmetric singlet and triplet hopping and pairing channels and minimizing the mean-field energy self-consistently, we obtain phase diagrams in the ($\tilde{J_x}, \tilde{J_z}$) plane in which only a few $Z_2$ states, several supporting gapless or flat-band spinon spectra, are stabilized. For these states we compute the spinon band structures, the low-temperature specific heat, and the dynamical spin structure factor, and we argue that the power-law specific-heat exponent is a diagnostic of the spinon nodal structure. A near-linear-in-temperature specific heat together with broad continua in the structure factor gives a fermionic-parton account of the gapless, fractionalized thermodynamics reported in DO materials such as $Nd_2ScNbO_7$, complementing the bosonic quantum-spin-ice picture of the Ce-based compounds. The work extends the fermionic-parton classification of DO pyrochlore QSLs beyond the $U(1)$ sector, where $Z_2$ topological order is realized equally naturally by fermionic and bosonic spinons.

In the temperature interval $T\sim 50 - 100 K$, the rate of electron-electron collisions in graphene devices may exceed the momentum relaxation rate due to disorder and electron-phonon scattering. In this regime, the motion of the electron liquid may be described by the hydrodynamic equations. In the hydrodynamic approximation, at the charge neutrality point the electric current is decoupled from the hydrodynamic flow, and the conductivity of the system is equal to the intrinsic conductivity of the electron liquid, $\sigma_0$. It was recently shown that the coupling of charge transport and hydrodynamic flow induced by the thermal fluctuations enhances the macroscopic conductivity of the system and results in very strong positive magnetoresistance (MR) at relatively weak fields. Here we develop a quantitative theory of the fluctuation mechanism of MR at charge neutrality and obtain analytic expressions for MR in graphene Hall bars. The functional dependence of MR on the magnetic field $H$ is sensitive to the Hall bar geometry and orientation relative to the current. We also account for the effect of momentum relaxation on MR.

Counterdiabatic driving provides a universal route to fast quantum control, but its standard formulation presupposes a Hamiltonian generator. We develop a Hamiltonian-free theory of the adiabatic gauge potential (AGP) for parameter-dependent unitary operators $U_\lambda$. Exact and regularized versions of the AGP follow from a Hermitian, banded linear system at a cost comparable to the Lanczos construction in the Hermitian case, requiring neither diagonalization nor a matrix logarithm. We demonstrate rapid convergence of the truncated Krylov approximation for the kicked top and for an integrable brickwork circuit built from unitary $\check{R}$ matrices, a setting in which no local effective Hamiltonian is available. Our results extend shortcuts to adiabaticity, and AGP-based diagnostics of chaos, to Floquet systems and quantum circuits.

Quantum impurity models are paradigmatic models of interacting quantum matter, as well as key computational primitives for modern electronic-structure methods. They describe a small subsystem of interacting fermions coupled to a large, noninteracting bath. We perform a comprehensive study of the computational complexity of simulating impurity models, delineating the boundary between classical and quantum tractability for this class of problems. Our main finding is that static properties of quantum impurity models can be calculated efficiently on a classical computer. Specifically, we give classical algorithms that (1) estimate the ground-state energy to additive precision $\delta$ in time $\mathrm{poly}(n,\delta^{-1})$, and (2) estimate the partition function at inverse temperature $\beta$ to relative precision $\delta$ in time $\mathrm{poly}(n,\beta,\delta^{-1})$, where $n$ is the system size. These results improve the previous best-known complexity for ground-state energy estimation from quasipolynomial to polynomial time, while establishing for the first time rigorous polynomial-time guarantees for simulating impurity models in thermal equilibrium. On the other hand, we find that simulating dynamical properties of impurity models is hard for classical computers but easy on a quantum computer. As a canonical example, we show that computing their nonequilibrium Green's functions captures the full power of quantum computation, even at finite temperature. Taken together, our results rule out superpolynomial quantum speedups for computing static properties, but provide an avenue for quantum advantage in simulating impurity physics out of equilibrium.

Electromagnetic duality in the toric code has order two at the level of anyon types and acts as a Hadamard-type logical transformation on the encoded quantum information. Here, we ask whether it can likewise be realized microscopically as an order-two Clifford operation. For the $\mathbb{Z}_2$ toric code, we prove that any locality-preserving Clifford realization of electric-magnetic exchange cannot have order two. Our proof is fully general and requires neither translation symmetry with restricted families of system sizes nor a fixed pairing between vertex and plaquette stabilizers. Geometrically, the proof locally emulates the unavoidable crossing between electric and magnetic strings, similar to a cross-cap in a non-orientable manifold. Extending the problem to the $\mathbb{Z}_N$ toric code, we find that an order-two Clifford realization exists for odd $N$, whereas it is impossible for even $N$. Our results show that the group law of an emergent electromagnetic duality need not lift faithfully to its microscopic Clifford realization.

Fermionic non-Gaussianity is a resource for universal quantum computation that can be generated by interactions in quantum many-body systems. Using the magic Rényi entropy (MRE) as a measure of non-Gaussianity, we derive its universal upper bound and Haar mean, proving that typical Haar-random states attain the maximal MRE density of $\ln(4/3)$ per Majorana in the large-system limit. We also show that the MRE can differ extensively between states with identical covariance matrices. To investigate how non-Gaussianity grows toward this maximal density, we evolve a Gaussian state in imaginary and real time under the Sachdev-Ye-Kitaev Hamiltonian. By varying the imaginary- and real-time durations, we identify a first-order transition marked by a kink in the MRE density and spontaneous breaking of the permutation symmetry among the four copies used to evaluate the MRE. This transition represents a qualitative change in the non-Gaussianity of the state that is not reflected in the thermal free energy.

The layered honeycomb $\alpha$-RuCl$_3$ has been much explored as a candidate to display unconventional cooperative magnetism between spin-orbit entangled $j_{\rm eff}=1/2$ Ru$^{3+}$ magnetic moments stabilized by strongly-frustrated, Kitaev and other bond-dependent anisotropic interactions. Most studies so far have focused on relatively large single crystals that undergo a structural phase transition from monoclinic to rhombohedral upon cooling below 150 K and a magnetic transition to zigzag order around 7 K. Here we study the magnetism of high-quality, very small (sub 100 $\mu$m diameter) single crystals, which remain monoclinic upon cooling to low temperatures and display a sharp magnetic transition at 14 K. Using highly-sensitive piezo-cantilever magnetic torque measurements in fields up to 16 T, we report a comprehensive study of the magnetic phase diagrams for magnetic field rotated in three orthogonal crystallographic planes. Our extensive torque data collected upon varying almost continuously the angular orientation of the field as well as the field magnitude, allows clear detection of phase transitions via anomalies in the raw torque data and its higher order derivatives with respect to both angle and field magnitude. The obtained magnetic phase diagrams show many differences compared to rhombohedral samples, displaying reduced rotational symmetry, substantially higher fields required to suppress the spontaneous magnetic order, and distinct field-induced phases. We provide a direct comparison of the torque data with mean-field calculations for magnetic Hamiltonians appropriate for $\alpha$-RuCl$_3$ allowing for the monoclinic lattice symmetry and propose minimal magnetic structure models for all explored regions of the magnetic phase diagrams.

Pyrite-type mineral hauerite MnS$_2$ is a magnetic insulator with localized $S=\frac52$ moments. Below 48 K, it develops a collinear antiferromagnetic order, accompanied by unit-cell doubling and breaking the inversion symmetry. We demonstrate that the latter gives rise to a ferroelectric polarization of up to 360 $\mu$C/m$^2$ rendering MnS$_2$ a type-II multiferroic. Microscopically, the electronic polarization originates from S$_2$ dimers that acquire a dipole moment induced by the frustrated magnetic ordering of neighboring Mn sites. We show that time-reversal symmetry leaves ferroelectric domains intact, and that domain switching necessitates overcoming a high energy barrier set by the magnetic exchange energy scale.

A recurring principle in many-body physics is that sufficiently distributed interactions or correlations lead to an effectively mean-field description. For fermionic Gaussian states, we establish a quantitative version of this principle directly at the level of Majorana covariance matrices. The main observation is that the admissibility condition for fermionic covariance matrices imposes a quantitative monogamy constraint on two-point correlations: a fixed region has only a bounded covariance budget to distribute among many disjoint regions. We use this principle in three directions. First, for quadratic fermionic Hamiltonians on finite simple graphs of high degree, we obtain product-state approximations to both the ground-state energy and the finite-temperature free energy, with error of order \(D^{-1/2}\) for \(D\)-regular graphs. Second, we prove a finite fermionic Gaussian de Finetti theorem: a \(k\)-copy Gaussian state that is \(n\)-exchangeable under graded fermionic copy permutations is \(O(k/n)\)-close in trace norm to the product of its one-copy marginal. In particular, infinite exchangeability within the Gaussian class implies exact product structure. Third, for spatial fermionic Gaussian states with exponentially clustering mutual information, we prove that the conditional mutual information across a separating buffer decays as \(O(r^{-1})\), and hence, by recoverability, the state admits an \(O(r^{-1/2})\) trace-norm approximation by a recovered state. These results show that product and de Finetti approximations and recoverability estimates for fermionic Gaussian systems can all be derived directly from covariance-level structure.

We report the synthesis and comprehensive investigation of single-crystalline Tb$_2$IrAl$_4$Ge$_2$ and Er$_2$IrAl$_4$Ge$_2$, the first Ir-based members of the $Ln_2M$Al$_4$Ge$_2$ family. Both compounds crystallize in the tetragonal Tb$_2$NiAl$_4$Ge$_2$-type structure (space group $I4/mmm$) and exhibit easy-axis magnetic anisotropy with the crystallographic $c$ axis as the preferred magnetization direction. Tb$_2$IrAl$_4$Ge$_2$ undergoes antiferromagnetic ordering below $T_N = 25$ K and develops a sequence of field-induced metamagnetic transitions accompanied by pronounced magnetotransport anomalies, including a nonlinear Hall response. In contrast, Er$_2$IrAl$_4$Ge$_2$ exhibits three successive zero-field magnetic transitions and a substantially richer low-temperature magnetic phase diagram comprising multiple competing field-induced phases confined to relatively modest magnetic fields. The differences between the Tb- and Er-based compounds demonstrate the wide range of magnetic behavior that can be realized within the \ce{Tb2NiAl4Ge2}-type structure. More broadly, the successful realization of Ir-based $Ln_2M$Al$_4$Ge$_2$ compounds considerably expands the accessible chemical space of this family and opens a route toward the exploration of related $4d$- and $5d$-based aluminogermanides.

In polar semiconductors the Fröhlich interaction is the dominant electron–phonon coupling, yet excitonic resonances in materials such as halide perovskites remain anomalously sharp. We show that standard frozen-center-of-mass treatments of the exciton–phonon problem miss the decisive kinematic degree of freedom: restoring the exact center-of-mass (COM) recoil reveals a universally open, parameter-free $1s\to1s$ absorption channel at recoil momentum $q_*=\sqrt{2M_{\rm ex}\hbar\omega_{\rm LO}}/\hbar$, whose rate scales as $N_{\rm LO}(T)$. We prove that this recoil channel is controlled by destructive electron–hole interference: the recoil linewidth vanishes with the mass asymmetry as $\gamma_{\rm LO}^{\rm recoil}\propto\mathcal{F}_{1s,1s}(q_*)^2$, and the elastic dressing obeys the exact suppression law $S_X/S_{\rm ind}=\eta^2(6-\eta^2)/5$ within the hydrogenic Fröhlich model. The theory establishes a hierarchy of scattering regimes. In mass-asymmetric materials (GaAs, $\eta=-0.74$) the recoil channel is active ($\gamma_{\rm LO}^{\rm recoil}=2.2$~meV); in mass-symmetric materials (FAPbI$_3$, $\eta=0$; MAPbI$_3$, $\eta=-0.11$) it is killed by interference (0.00 and 0.12 meV), showing that the observed 27–40 meV perovskite linewidths cannot be accounted for by COM recoil and therefore require internal-state-changing and other inelastic channels, of which the constructive, $\eta$-robust $1s\to np$ resonance is the leading candidate within the present model. The Fröhlich constant $\alpha$ alone is therefore insufficient as a figure of merit: after projection onto the correlated exciton, the controlling parameters are $\eta$, $q_*a_X$, and the Rydberg detuning.

In a polar material, a neutral exciton couples to phonons through the sum of the electron and hole deformation potentials. Because the total source vanishes by charge neutrality, the elastic exciton-phonon vertex is regularized by electron-hole interference. Here we determine the non-perturbative fate of this interference by exact diagonalization of a Holstein-exciton model. By parameterizing the mass asymmetry to decouple it from the small-polaron atomic limit, we map a regime map comprising an internal dressing crossover and a dissociation boundary. We prove analytically and verify numerically that for equal masses, the symmetric exciton ground state is protected from phonon dressing by an exact exchange selection rule, provided the phonon source is odd under electron-hole exchange (the neutral case). As mass asymmetry increases, this selection rule is broken and the exciton acquires a strong local polaronic cloud. We show that the dissociation boundary, conversely, is set by a global energy balance between Coulomb binding and polaronic stabilization, and is nearly independent of the internal dressing. Paradoxically, the very symmetry that protects the exciton from dressing denies it polaronic stabilization, driving it toward dissociation at strong coupling. We discuss these results in the context of lattice exciton-polaron models and their implications for sharp versus broad excitonic lines in mass-symmetric versus mass-asymmetric polar semiconductors.

The interplay between electronic and structural degrees of freedom underpins many emergent phenomena in quantum materials, yet magnetoelastic coupling in metallic systems is typically weak and confined to low temperatures or microscopic length scales. Here, we report giant magnetoelastic coupling slightly above room temperature in the uranium-based intermetallic compound UIr$_4$Al$_{15}$. Using temperature-dependent single-crystal X-ray diffraction together with anisotropic magnetic susceptibility measurements, we directly resolve subtle but reproducible structural distortions coupled to magnetic alignment. Despite the absence of crystallographic symmetry breaking, pronounced anomalies emerge in lattice parameters and selected chemical bond distances near the magnetic transition region, revealing an unusual sensitivity of the crystal structure to magnetic orientation. The coupling enables direct probing of how atomic distances and local chemical bonding govern the electronic and magnetic states in a bulk intermetallic material. Our results establish UIr$_4$Al$_{15}$ as a rare platform in which magnetism and lattice distortions are strongly intertwined near room temperature, opening new opportunities for magnetically responsive quantum materials and functional magnetic sensing applications.

Vacancy ordered double perovskites (VODPs) have been known for more than 100 years, but their exact crystal structures and magnetic ground state remained controversial till date. Anhydrous VODP iridates ($A_2$Ir$X_6$; $A$ = K$^+$, (NH$_4$)$^+$, Cs$^+$, Rb$^+$, and $X$ = F$^-$, Cl$^-$, Br$^-$), having $face-centered~cubic$ (fcc) antiferromagnetic ground state, offer a chemically well-defined platform to investigate the influence of on-site Coulomb repulsion, crystal field, spin-orbit coupling, and competing Heisenberg and Kitaev interactions. Interestingly, among these, the Na-based VODP iridates seem to possess an unusual hydration dependent structural and magnetic uncertainty. As a result, a cubic Na$_2$IrCl$_6$ system having fcc antiferromagnetism could not be stabilized ever. Here, for the first time, we report the synthesis and comprehensive characterization of anhydrous Na$_2$IrCl$_6$ single crystals having fcc structure with antiferromagnetic transition temperature of 1.91 K. Thermogravimetric analysis establishes the absence of lattice water and also demonstrates thermal stability of the crystals up to 453 K. The cubic phase reported here contrasts with previously described 'anhydrous' monoclinic Na$_2$IrCl$_6$ and highlights the strong structural and physical property relationship in Na-based VODP iridates. This new material offers an exciting playing ground for exploring another potential perfect $J_{eff}$ = $\frac{1}{2}$ octahedra and the consequent strong Kitaev interaction within the nearest-neighbor (nn) pairs of Ir ions.

The Verwey transition in magnetite is a benchmark electronically driven phase transition that is highly sensitive to lattice imperfections and external perturbations. Doping, deviations from oxygen stoichiometry, and irradiation-induced point defects are known to lower the Verwey transition temperature, $T_{\rm V}$. By contrast, the role of remanent strain fields and extended defect structures generated by uniaxial stress has remained largely unexplored. Here we combine dark-field x-ray microscopy (DFXM) and ac magnetic susceptibility to determine how strain-induced defects affect the Verwey transition in stoichiometric single-crystalline magnetite after uniaxial compression and unloading. The DFXM measurements were performed on two samples compressed along the same $[011]$ direction: loading to $200~\mathrm{MPa}$ generated stable line-like defects and remanent strain fields, whereas loading beyond the fracture threshold produced denser defect networks and mechanical fracture. To test the effect of a different loading geometry, we also measured the ac susceptibility of a sample fractured by compression along $[001]$. Real-space DFXM imaging, lattice-orientation mapping, and residual strain mapping show substantial remanent structural disorder after compression. Nevertheless, neither the transition temperature $T_{\rm V}$ nor the sharpness of the transition changes measurably in any of the compressed or fractured samples. This behavior contrasts with the strong suppression of $T_{\rm V}$ by point-like disorder. Our results show that extended line-like defects and remanent strain fields produced by plastic deformation do not measurably perturb the macroscopic electronic ordering responsible for the Verwey transition, thereby distinguishing the effects of point defects from those of extended slip-related defects in magnetite.

The composite-fermion framework maps the strongly correlated fractional quantum Hall state onto a weakly interacting integer quantum Hall state in a reduced effective magnetic field. We ask how this framework is modified for fractional Chern insulators, where the role of a uniform magnetic field is replaced by the nonuniform Berry curvature of a Chern band. Specifically, we construct composite-fermion wave functions for Jain states and their quasiparticles and quasiholes in Aharonov-Casher bands, a widely used model for ideal Chern bands. We find that these states overlap closely with exact eigenstates over a broad range of field modulation. Using these wave functions, we demonstrate that the emergent composite-fermion band structure goes beyond the conventional picture of effective Landau levels, correctly capturing the quasiparticle dispersion. Remarkably, we find that an isolated quasiparticle band carries a total Berry flux that is different from a Landau level. These results establish a composite-fermion description for mobile fractional Chern insulator anyons and provide a framework to understand their stability.

We study mixed-state entanglement in Gibbs states with strong $\mathrm{SU}(2)$ symmetry, focusing on locally interacting spin systems with ferromagnetic interactions. Our main result is to show that finite-temperature ordering transitions are associated with entanglement transitions, and therefore the steady state of strongly symmetric Lindbladians can exhibit entanglement transitions. While in the paramagnetic phase it is known that the distillable entanglement and logarithmic entanglement negativity between two halves of a large system grow logarithmically with the square root of the number of spins, we show that in ferromagnetic phases these quantities grow parametrically faster with system size. To arrive at this result we first establish relations between these mixed-state entanglement measures and spin correlations in states that are singlets under global $\rm{SU}(2)$ symmetry transformations. We then introduce a semiclassical theory for $\rm{SU}(2)$ singlet thermal states. While the global singlet constraint generally enters this theory as a complicated function of the full semiclassical spin configuration, we show that in large $S$ limit it simplifies drastically to a Gaussian suppression of total magnetization in disordered phases as well as in ordered phases in the vicinity of continuous thermal phase transitions. This leads us to a field theory describing spin correlations in the singlet sector. Using this we determine the behavior of various probes of mixed-state entanglement at low and at high temperatures, supporting our analytical results using numerical Monte Carlo simulations of a three-dimensional lattice realization of our semiclassical theory. We also use exact numerics in one-dimensional spin-$1/2$ systems to confirm our predictions for the scaling of mixed-state entanglement with correlation length and system size in the paramagnetic phase.

Fine features in the Fermi surface geometry, such as nearly cylindrical or nearly paraboloidal strips or local flattenings, are examined as regards their effect on the electronic, mainly galvanomagnetic, properties of metals. It is shown that under certain conditions, these features may significantly change the way a conventional normal metal or a layered structure with metallic conductivity responds to high- frequency external disturbances. All of the effects considered appear to be very sensitive to the disturbance propagation direction and/or to that of the external magnetic field. Experimental possibilities of observing the described effects are discussed.

Strain offers a direct route to control electronic phases by altering bond lengths, hopping amplitudes, and lattice symmetries. These aspects make electron-phonon (e-ph) coupled systems a natural setting to study strain-induced effects. The Su-Schrieffer-Heeger (SSH) Hamiltonian describes the coupling between itinerant electrons and lattice degrees of freedom that modulate hopping and is thus expected to be strongly affected by strain fields. At half-filling and on a bipartite lattice, the SSH interactions drive dominant bond-order-wave (BOW) correlations at low- temperature in which short bonds with high kinetic energy alternate with long bonds with low kinetic energy along four possible patterns. We model uniaxial strain through anisotropic hopping, which breaks the $90^\circ$ rotational symmetry and reduces the BOW phase degeneracy to two. We also include an on-site Hubbard U that promotes antiferromagnetic correlations that are also (weakly) driven by the SSH interaction itself. We map out the half-filled phase diagram in the plane of the e-ph and Hubbard couplings, and determine the critical temperature of BOW formation. Using analytic continuation, we also evaluate the spectral function and demonstrate directionally dependent gap formation in the BOW phase

Non-ergodic quantum many-body dynamics offers a route to persistent quantum coherence far from equilibrium, beyond the conventional expectations of thermalizing statistical mechanics. Most known examples have been identified through intuition, analogy, or numerical search, rather than by systematic Hamiltonian design. This leaves few general methods for engineering robust non-ergodic dynamics in disorder-free interacting quantum many-body systems, especially in higher dimensions where enhanced connectivity generally disfavors ergodicity breaking. Here, we use an eigenstate-to-Hamiltonian construction approach to systematically engineer two-dimensional quantum spin Hamiltonians with tunable non-ergodic properties. Starting from a common parent model and input eigenstate, we construct two target Hamiltonians on the square lattice that differ in their interaction geometry: axial versus diagonal. We show that the resulting interaction geometry and coupling pattern control the Hilbert-space structure and dynamics. The axial model forms a connected Hilbert-space network and exhibits an anisotropy-driven crossover from ergodic to non-ergodic behavior through the suppression of resonances. In contrast, the diagonal model exhibits Hilbert-space fragmentation and, within its largest irreducible sector, signatures of quantum many-body scar dynamics including towers of highly localized, low-entanglement eigenstates, and long-lived coherent revivals. These results establish a direct link between Hamiltonian design, Hilbert-space network structure, and emergent non-ergodic dynamics.

The microscopic mechanism governing the zero-field incommensurate magnetic order in the honeycomb cobaltate $\mathrm{BaCo}_2(\mathrm{AsO}_4)_2$ remains a significant unresolved problem, particularly concerning the relative contributions of bond-directional Kitaev-type interactions and exchange frustration. This study investigates an extended $J_1\text{--}K\text{--}\Gamma\text{--}\Gamma'\text{--}J_2\text{--}J_3$ model, which incorporates XXZ-type exchange anisotropies on the honeycomb lattice. Nearest-neighbor parameters are constrained by ab initio electronic structure calculations. By integrating the analytical Luttinger-Tisza approach with exact diagonalization calculations under twisted boundary conditions, we delineate the classical and quantum phase diagrams across the $(J_2, J_3)$ parameter space. We demonstrate that the stabilization of the experimentally observed incommensurate spiral phase, propagating along the $\Gamma\to M$ direction, does not necessitate an anomalously dominant Kitaev coupling. Instead, this phase arises naturally from the synergistic interplay between exchange frustration, driven by further-neighbor couplings ($J_2, J_3$), and intermediate off-diagonal bond anisotropies ($\Gamma, \Gamma'$). In the quantum regime, we elucidate the competition between this incommensurate manifold and an out-of-plane ferromagnetic ($\mathrm{FM}_z$) phase, which is selectively stabilized via a quantum order-by-disorder mechanism. Our findings reconcile conflicting interpretations of the magnetic interactions in $\mathrm{BaCo}_2(\mathrm{AsO}_4)_2$ and establish the microscopic origin and stability range of its incommensurate ground state.

We investigated the influence of antiferromagnetic (AFM) order on the near-infrared optical re- sponse of SmFe3(BO3)4 by polarization-resolved, magneto-optical spectroscopy. Below the Néel temperature, we observed pronounced magnetic linear dichroism at the 4f -4f transitions of Sm3+. By rotating the order parameter of the easy-plane AFM ground state using magnetic fields, we demonstrated the magnetic field control of linear dichroism, and deduced polarization selection rules. In addition, we detected non-reciprocal directional dichroism for several 4f -4f transitions. The non-reciprocal absorption appears in the symmetry-allowed toroidal geometry when the in- plane magnetic field is normal to one of the two-fold rotation axes. These results indicate a strong interference between electric- and magnetic-dipole excitations for transitions showing non-reciprocal absorption. The observed optical anisotropies provide a promising path to detect the in-plane orien- tation of the AFM order, enabling imaging and time-resolved studies of the AFM order parameter in rare-earth ferroborates.

The discovery of pressure-induced superconductivity in Ruddlesden–Popper (RP) nickelates has stimulated extensive interest in high-T$_c$ superconductors. Here, we systematically study the electronic properties of the quadlayer RP nickelate La$_5$Ni$_4$O$_{13}$ under ambient pressure, 5% isotropic compressive strain, and 4% $c$-axis uniaxial strain using density functional theory (DFT) and random phase approximation (RPA) calculations. DFT calculations show that isotropic strain broadens the Ni-$e_g$ bands and induces charge transfer from O-$p$ to Ni-$d$ orbitals, whereas $c$-axis uniaxial strain selectively shifts the $d_{z^2}$-derived bonding1 band upward while leaving the $d_{x^2-y^2}$ dispersion nearly unchanged. From Wannier downfolding, we construct a quadlayer two-orbital model that reproduces the low-energy Ni-$e_g$ bands. Our model reveals that under ambient pressure and 5% isotropic strain, the Fermi surface consists of two electron pockets ($\alpha$ and $\delta$) and three hole pockets ($\beta$, $\beta^{\prime}$, and $\beta^{\prime \prime}$), while under uniaxial strain, a $\gamma$ hole pocket with $d_{z^2}$ orbital character emerges. RPA calculations reveal that the leading spin response shifts from $\mathbf{q}\approx(2\pi/3,2\pi/3)$ at ambient pressure to $\mathbf{q}\approx(\pi,\pi)$ under both strain conditions and is enhanced under $c$-axis compression. These results suggest that $c$-axis compression may provide a favorable route to superconductivity in the quadlayer nickelate analogous to that in bilayer and trilayer nickelates.

Open quantum systems can exhibit inherently mixed quantum orders, such as strong-to-weak spontaneous symmetry breaking (SW-SSB), which have no analogue in pure states. It is generally expected that a finite-depth local quantum channel cannot induce a phase transition to SW-SSB in one spatial dimension. We circumvent this obstruction by introducing a long-range quantum channel, which implements two-body dephasing on pairs of sites with probability falling off according to a power-law in the site separation. Applying this channel to a one-parameter family of matrix product states interpolating between trivial and symmetry-protected topological (SPT) phases, we construct a phase diagram that hosts trivial, mixed SPT, and SW-SSB phases with respect to Rényi-2 diagnostics. Notably, the mixed SPT phase is distinct from previously studied decohered SPT phases: it hosts two logical qubits and exhibits nonvanishing Rényi-2 string order, despite vanishing conventional string order. Through a series of mappings to a classical statistical mechanics model, we establish a direct connection between the loss of logical information and the onset of SW-SSB in this model. Finally, we consider the feasibility of experimental realization of the phenomena we have studied. We emphasize that our family of mixed states can be tuned to regimes of high purity, substantially reducing measurement overhead and enabling their experimental realization and detection on near-term quantum hardware.

Strong-to-weak spontaneous symmetry breaking (SW-SSB) is a distinctive phenomenon of mixed quantum states, characterized by nonlinear long-range order associated with strong symmetry. In realistic open quantum systems, however, strong symmetry is macroscopically fragile and can be explicitly reduced to weak symmetry through local charge exchange with the environment. In this paper, we investigate how the SW-SSB order decays under such strong-symmetry-breaking Liouvillian dynamics. For discrete $\mathbb{Z}_2$ symmetry, a local symmetry-breaking perturbation drives an exponential decay of the Rényi-1 long-range correlator, revealing the fragility of discrete SW-SSB order. By contrast, for continuous $U(1)$ symmetry, local charge exchange broadens the distribution over symmetry-charge sectors and leads to parametrically slower algebraic relaxation. We establish a rigorous algebraic lower bound on the connected Rényi-1 long-range correlation, demonstrating the robustness of this slow relaxation. In the thermodynamic limit, we further uncover a two-stage dynamical scaling: $\tilde{R}_1\sim t^{-1}$ at early times and $\tilde{R}_1\sim t^{-1/z}$ at long times, with $z$ set by the underlying hydrodynamic dynamics. As a numerical verification, we consider fermionic chains with $z=2$ and $z=4$, which are excellent agreement with the theoretical predictions.

At high temperature instantons form a dilute gas, so in QCD-like theories the breaking of the anomalous $U(1)_A$ symmetry is given by integral powers of the anomalous determinant, $\sim (\det \Phi)^{Q}$, where $\Phi\sim \overline{q}_L q_R$ is bilinear in the quark fields, and with untwisted boundary conditions, the topological charge, $Q$, is an integer. A syncretic model is constructed, which is manifestly "beyond Landau". In the chiral limit, at temperatures above the chiral phase transition, $T > T_\chi$, only integral powers of the anomalous determinant appear. Below $T_\chi$, following 't Hooft et al. I assume that the topological charge $Q$ is fractional, as an integer times $1/N_c$, where $N_c$ is the number of colors. I suggest that consequently, fractional powers of the anomalous determinant appear in the chiral effective Lagrangian. For $N_f$ degenerate flavors, this generalizes the Witten-Veneziano term, valid for small $N_f/N_c$, to arbitrary $N_f/N_c$. In this model the chiral phase transition is generically of second order. The two exceptions are for one flavor, where it is probably crossover, and three flavors, where it could well be weakly first order. This can be tested in lattice QCD with $2+1$ flavors by comparing the (known) temperature dependence of the difference of the $\pi^a$ and $a_0^a$ propagators, to the chiral condensate of the strange quark, between $T_\chi$ and $\sim 2 \, T_\chi$. Analogous measurements are possible for one to four degenerate flavors about $T_\chi$. Lastly, I propose an operator for baryon number in the symmetric phase.

Recent work has shown that quantum double models can be used to circumvent the Bravyi-Koenig bound. In particular, this is achieved through code-switching protocols in which non-Pauli stabilizer phases appear as intermediate codes. We introduce the $X\mathcal C^{(k)}_d$ stabilizer formalism, which generalizes the Pauli stabilizer formalism by combining Pauli-$X$ operators with diagonal operators drawn from a fixed level $k$ of the Clifford hierarchy on prime-dimensional qudits. This yields a natural class of beyond-Pauli stabilizer models, including many twisted quantum double phases. We classify a large class of these $X\mathcal C^{(k)}_d$ stabilizer states, showing that they are uniform superpositions over affine-linear subspaces with diagonal phases. In particular, when the stabilizers of a state require operators from level $k$ of the Clifford hierarchy, we show that the diagonal gates required to produce the phases in the wavefunction sit one level higher. We further show that every 2D twisted quantum double ${\cal D}^\omega(\mathbb{Z}_p^n)$ with $\omega$ a product of type-III cocycles and $p$ an odd prime admits a realization using only Clifford ($k=2$) stabilizers, and we conjecture that phases where $\omega$ contains a type-I or type-II cocycle require level-$p$ Clifford-hierarchy stabilizers for $p$-dimensional qudits. Finally, we demonstrate that a pair of qudit toric codes may be deterministically prepared in a logical magic state by measuring $X\mathcal C^{(k)}_d$ stabilizers. Together, these results provide a concrete stabilizer framework for topological codes beyond Pauli stabilizer models and their logical gates.