arXiv subjects

Shinsei Ryu

Publications and source records attributed to Shinsei Ryu.

At least 19 recordsLinked to original sources

arXiv2026

Bootstrapping Symmetries in Quantum Many-Body Systems from the Cross Spectral Form Factor

Symmetries play a central role in quantum many-body physics, yet uncovering them systematically remains challenging. We introduce a bootstrap framework to reconstruct the representation theory of hidden finite group symmetries of quantum many-body lattice Hamiltonians, using only a known symmetry subgroup $N$ and spectral correlations between its sectors. We introduce the cross spectral form factor (xSFF) as a subgroup-resolved diagnostic of hidden symmetry, computed via exact diagonalization to seed the bootstrap. Applying constraints from these data alongside the algebraic conditions of the fusion rules, our bootstrap sharply restricts candidate groups $G$. Without prior assumptions about $G$, our method can systematically recover its representation-theoretic data, including the number and dimensions of irreducible representations, their branching rules with respect to $N$, the fusion algebra, and the full character table. This framework applies to chaotic and integrable systems and accommodates unitary and anti-unitary symmetries. Through examples, we demonstrate that $G$ can be uniquely identified. Our bootstrap recovers the $\mathbb{Z}_4$ symmetry at the self-dual point of the three-state quantum torus chain, detects signatures of projective representations in the effective Hamiltonian of the driven Bose-Hubbard model, and rediscovers the $η$-pairing $\mathrm{SO}(4)$ symmetry of the one-dimensional Fermi-Hubbard model. Leveraging the universal random-matrix ramp in chaotic systems, we demonstrate the possibility of ramp-only bootstrap alongside an example with hidden commuting symmetries. We establish the xSFF as a diagnostic for conserved order parameters in a symmetry-breaking spin-$1$ chain and introduce an ancilla-assisted measurement circuit for experimental realization. Our framework establishes a practical route to identify symmetries from dynamical spectral observables.

quant-ph↗

arXiv2026

Universal Eigenvector Statistics of Non-Hermitian Random Matrices

Eigenvector overlaps quantify nonorthogonality and govern the response and dynamics of non-Hermitian systems. We extend the universality of non-Hermitian random matrices to the statistics of these overlaps. We obtain analytical expressions for eigenvector overlaps in the spectral bulk and near the origin, covering ten symmetry classes in the limit of large matrix size. Using fermionic replica nonlinear $σ$ models, we relate these overlaps to Hermitian level statistics, symmetry class by symmetry class and topological sector by topological sector. Numerical calculations in various physical models support the universality of the normalized overlaps in the regimes studied. Our work establishes a duality between Hermitian level statistics and non-Hermitian eigenvector overlaps.

cond-mat.stat-mech↗

arXiv2026

Tripartite entanglement in chaotic eigenstates

It is now well-established that classical statistical mechanics emerges from the entanglement structure of quantum chaotic systems, as quantified by the (subsystem) eigenstate thermalization hypothesis (ETH). While this statement rests on the well-studied bipartite entanglement of the eigenstates of such systems, recent years have shown that many-body states are often characterized by multipartite entanglement, raising the question: what are the universal multipartite entanglement features of chaotic eigenstates? We answer this question in part by studying a tripartite generalization of the ergodic bipartition ansatz through the lens of two tripartite entanglement probes, the Rényi tripartite multi-entropy and the Rényi reflected entropy. We derive leading-order analytical expressions for the ensemble averages of both quantities using a saddle-point analysis. Beyond these measures, we obtain the average of the Rényi-2 reflected density matrix, $ρ_{AA^*}^{(2)}$,which controls the Rényi-2 reflected entropy. We show that $ρ_{AA^*}^{(2)}$ in a chaotic eigenstate is well-described by this ensemble average which, unlike an ordinary reduced density matrix, takes three qualitatively distinct forms across subsystem-size regimes, which may be viewed as a tripartite generalization of subsystem ETH. We benchmark our analytical predictions against exact diagonalization of the mixed-field Ising model.

cond-mat.str-el↗

arXiv2026

Duality between the level statistics of Hermitian and non-Hermitian random matrices

Random matrix theory describes complex quantum systems statistically, with symmetry as its organizing principle. We uncover an exact duality between the level statistics of Hermitian and non-Hermitian random matrices in the large-$N$ (matrix size) limit. It acts class by class: the two replica partition functions, given by fermionic nonlinear $σ$ models, are related by analytic continuation. Applied to the three Wigner--Dyson classes, the duality yields the universal bulk eigenvalue pair-correlation functions of non-Hermitian random matrices. This establishes a non-Hermitian counterpart of Dyson's threefold way, organized by transposition symmetry: generic complex, complex symmetric, and complex self-dual matrices. The dissipative spectral form factors of these classes follow in closed form as well. Applied to the seven nonstandard Altland--Zirnbauer classes, the duality yields the exact spectral densities near the origin, the non-Hermitian hard-edge statistics. Most of these statistics were previously known only numerically. Exact diagonalization confirms the analytical predictions, and physical models demonstrate their universality. We expect these results to be the tip of a deeper correspondence between Hermitian and non-Hermitian random matrix theory.

cond-mat.stat-mech↗

arXiv2026

Exact joint eigenvalue densities of non-Hermitian random matrices are Calogero scattering states

Determining exact joint eigenvalue densities is central to random matrix theory. We solve this long-standing problem for non-Hermitian matrices with transposition symmetry (complex symmetric and complex self-dual) at arbitrary matrix size. Up to a Vandermonde factor, they are scattering-state wave functions of the Calogero model, a line of particles interacting through an inverse-square potential, with the coupling strength set by the symmetry. In contrast to many previously known joint densities, the densities cannot be written as a gas of eigenvalues with pairwise interactions. We further compute the complex level spacing distributions and two-point spectral correlation functions, which carry power-law tails, absent in a Coulomb gas. Our results shed light on the interplay among random matrices, integrability, and symmetry.

cond-mat.stat-mech↗

arXiv2026

Dissipation-enhanced scrambling in the SYK model coupled to a lossy cavity

We study the Yukawa-Sachdev-Ye-Kitaev model, a disordered model of $N$ Majorana fermions and $R=γN$ bosons in which the bosons are linearly coupled to independent realizations of SYK $p$-body interactions, in the presence of dissipation, modeled by a Lindblad master equation. Motivated by recent proposals for implementing SYK models in quantum simulators, we focus on bosonic leakage at rate $κ$. Initializing the system in the steady state, we analyze the late-time fermionic relaxation rate and the Lyapunov exponent, solving the large-$N$ theory both numerically and for $p$ large, finding a rich landscape of dynamical behaviors. Most notably, the Lyapunov exponent remains positive for every value of $κ$ and, for $p>2$, can even grow as $κ$ increases. The QED case $p=2$, which lies between the fully chaotic regime $p>2$ and the integrable case $p=1$, exhibits special features. We also identify a critical value of the boson-to-fermion ratio $γ_c \approx 2/p^2$ separating distinct dynamical regimes.

quant-ph↗

arXiv2026

Anomalous entanglement scaling from eigenvector nonorthogonality in critical non-Hermitian free fermions

Entanglement carries universal content that labels phases and critical points. We study the entanglement entropy of the steady states of critical non-Hermitian free-fermion chains. It scales logarithmically with subsystem size, but the coefficients vary continuously with the parameters and form a Rényi family that no single central charge can reproduce. We trace this anomaly to an ``imaginary'' Dirac point, a crossing in the imaginary part of the energy where the occupied state switches between two Bloch states. Their nonorthogonality weakens the occupation discontinuity and lowers the logarithmic coefficient. A low-energy expansion yields closed-form coefficients in excellent agreement with lattice numerics in various one-dimensional critical steady states. Remarkably, weak real onsite disorder leaves this logarithmic scaling intact and enhances the entanglement. Our results provide a generic understanding of entanglement in critical non-Hermitian free-fermion steady states.

cond-mat.mes-hall↗

arXiv2026

Ideal Bands in Tight-Binding Models

A band is called ideal when its Dirichlet functional saturates the topological lower bound. We study ideal bands in finite-band tight-binding models with conventional two-dimensional lattice translation symmetries, allowing the bands to have non-flat dispersion. We first provide an analytic construction of isolated Chern-ideal bands with Chern number $|\mathrm{Ch}|=1$ in finite-band models with exponentially decaying hopping. This construction applies only when at least two orbitals have different embedded positions (modulo lattice vectors), complementing the previously known construction for $|\mathrm{Ch}|>1$. We then show that isolated Chern-ideal bands with any nonzero Chern number cannot exist in finite-band models with finite-range hopping, regardless of the embedded orbital positions. The conclusion holds even if there are isolated band touching points, as long as the Berry curvature does not diverge anywhere in the Brillouin zone. We finally generalize the conclusions to Wilson-loop-ideal bands with zero total Chern number, such as Kane-Mele $\mathbb{Z}_2$-ideal bands.

cond-mat.mes-hall↗

arXiv2026

Local-to-Global Entanglement Dynamics by Periodically Driving Impurities

We study the entanglement dynamics of one-dimensional fermionic chains subject to a local Floquet drive of a two-site impurity, and uncover a sharp transition in the entanglement dynamics set by the driving period $T$. For large periods, the entanglement entropy (EE) grows linearly in time, signaling a heating phase with volume-law entanglement; below a critical period $T_\ast$, the EE instead grows subextensively, characteristic of a local quantum quench. We establish this dichotomy in two complementary settings: a gapless nearest-neighbor hopping chain, where a single transition separates logarithmic from volume-law growth, and a gapped Su-Schrieffer-Heeger (SSH) chain, whose two-band structure yields a richer phase diagram with multiple area-to-volume-law transitions. In the noninteracting limit, we trace these transitions analytically to quasienergy folding in the single-particle Floquet spectrum: a single $π$-gap closure for the NN chain, and a sequence of foldings at both 0- and $π$-gaps for the SSH chain, yielding the alternating pattern of heating and non-heating phases. We further show that the so-called ``average energy" operator furnishes a many-body diagnostic of the transition, remaining local in the non-heating phase but developing non-local couplings in the heating phase. For the gapless chain, using extensive matrix-product-state simulations, we demonstrate that the non-heating phase and its subextensive entanglement growth survive weak interactions over numerically accessible timescales. Our results establish local Floquet engineering as a route to emergent bulk phenomena, offering a new perspective on energy localization and thermalization in driven many-body systems.

quant-ph↗

arXiv2026

Diffusive Dynamics of Nonstabilizerness

Symmetries shape the quantum-information dynamics of many-body systems, but their effect on nonstabilizerness, the resource complementary to entanglement, is less understood. We compute the stabilizer Rényi entropy, a measure of nonstabilizerness, in $\mathrm{U}(1)$-symmetric one-dimensional random circuits. The disorder-averaged dynamics is captured by a four-replica tensor network, which we evaluate by $S_4$-adapted infinite time-evolving block decimation (iTEBD) directly in the thermodynamic limit. Together with a hydrodynamic argument, our results identify a diffusive universality class for the late-time approach of nonstabilizerness to its random-state value, with the stabilizer Rényi entropy gap closing as $1/t$. The same scaling is verified in an energy-conserving nonintegrable Ising chain. More broadly, our framework provides a hydrodynamic perspective on nonstabilizerness generation and offers insight into the design of approximate Haar-random states in Hamiltonian dynamics.

quant-ph↗

arXiv2026

Unveiling Topological Fusion in Quantum Hall Systems from Microscopic Principles

Establishing the fusion rules of anyonic quasiparticles in fractional quantum Hall fluids is essential for understanding their underlying topological order. Building on the conjecture that key topological properties are encoded in the "DNA" of candidate many-body wave functions - that is, the pattern of dominant orbital occupations restricted to a finite number of lowest Landau levels - we propose a combinatorial framework that derives these fusion rules directly from microscopic data. By extending Schrieffer's counting argument and introducing classes of topological excitations, our framework provides a unified route to the fusion rules for both Abelian and non-Abelian excitations. This approach elucidates the emergence of topological features from first principles in both fermionic and bosonic systems.

cond-mat.mes-hall↗

arXiv2026

Fermi Surface Geometry from Charge Fluctuations in Three-Dimensional Metals

For three-dimensional non-interacting multi-band metals, we show that important information about the shape and the quantum geometry of Fermi surfaces is encoded in the subleading logarithmic term of bipartite charge fluctuations. This logarithmic term is related to the dimensionless $|\mathbf{q}|^3$-coefficient of the structure factor in momentum space, and both quantities can be expressed as Fermi surface integrals of the Fermi surface curvature tensor and the quantum metric tensor. When the real-space partition surface is a quadric (i.e., sphere or ellipsoid), the logarithmic coefficient satisfies a topological bound depending only on the Euler characteristic and the Chern number of the Fermi surface, illustrating a non-trivial interplay between topology and quantum topology in multi-band metals.

cond-mat.mes-hall↗

arXiv2026

Corner Charge Fluctuations in Higher Dimensions

Measuring charge fluctuations within a subregion provides a powerful probe of quantum many-body systems. In two spatial dimensions, the shape dependence of the dimensionless corner contribution encodes universal data of quantum critical points and reveals observables of quantum geometry in various quantum phases. Here, we systematically extend this framework to higher dimensions. In three dimensions, we derive the universal angle dependence associated with trihedral corners of a generic parallelepiped and benchmark the predictions against Monte Carlo simulations of lattice models at the O(3) quantum critical point. We further identify a wedge-corner contribution that directly probes the quantum metric, supported by numerical results for a lattice Weyl semimetal model. More generally, we obtain angle functions for polyhedral corners of arbitrary parallelotopes in general dimensions and clarify the scaling of the corner contribution across phases of matter. While insulators and conformal critical points exhibit similar behavior across dimensions, metals display a characteristic even-odd dimensional effect.

cond-mat.str-el↗

arXiv2026

Wilson-Loop-Ideal Bands and General Idealization

Quantum geometry is universally bounded from below by Wilson-loop windings. In this work, we define an isolated set of bands to be Wilson-loop-ideal, if their quantum metric saturates the Wilson-loop lower bound. The definition naturally incorporates the known Chern-ideal and Euler-ideal bands, and allows us to define other types of ideal bands, such as Kane-Mele $Z_2$-ideal and inversion-fragile-ideal bands. In particular, we find that in the case of zero total Chern number, an isolated WL-ideal set of two bands with non-singular nonabelian Berry curvature and nontrivial normal Wilson-loop winding always admits a Chern-ideal gauge, without the need of a global good quantum number (such as spin). This enables the direct construction of new topologically ordered states, such as fractional topological insulator wavefunctions. We further propose a general framework of constructing monotonic flows that achieve Wilson-loop-ideal states starting from non-ideal bands through band mixing, where Wilson-loop-ideal states are not energy eigenstates but have smooth projectors similar to isolated bands. We apply the constructed flows to the realistic model of $3.89^\circ$ twisted bilayer MoTe$_2$, a moiré Rashba model and another moiré time-reversal-breaking models, and numerically find Chern-ideal, $Z_2$-ideal and inversion-fragile states, respectively, with relative error in the integrated quantum metric below $5\times 10^{-3}$. Our exact-diagonalization calculations on the numerically ideal states demonstrate the potential of our general definition of Wilson-loop-ideal bands and general procedure of constructing Wilson-loop-ideal states for future study of novel correlated physics.

cond-mat.mes-hall↗

arXiv2026

Probing chiral topological states with permutation defects

The hallmark of two-dimensional chiral topological phases is the existence of anomalous gapless modes at the spatial boundary. Yet, the manifestation of this edge anomaly within the bulk ground-state wavefunction itself remains only partially understood. In this work, we introduce a family of multipartite entanglement measures that probe chirality directly from the bulk wavefunction. Our construction involves applying different permutations between replicas of the ground state wavefunction in neighboring spatial regions, creating "permutation defects" at the boundaries between these regions. We provide general arguments for the robustness of these measures and develop a field-theoretical framework to compute them systematically. While the standard topological field theory prescription misses the chiral contribution, our method correctly identifies it as the chiral conformal field theory partition function on high-genus Riemann surfaces. This feature is a consequence of the bulk-edge correspondence, which dictates that any regularization of the theory at the permutation defects must introduce gapless boundary modes. We numerically verify our results with both free-fermion and strongly-interacting chiral topological states and find excellent agreement. Our results enable the extraction of the chiral central charge and the Hall conductance using a finite number of wavefunction replicas, making these quantities accessible to Monte-Carlo numerical techniques and noisy intermediate-scale quantum devices.

quant-ph↗

arXiv2026

Exponentially Accelerated Sampling of Pauli Strings for Nonstabilizerness

Quantum magic, quantified by nonstabilizerness, measures departures from stabilizer structure and underlies potential quantum speedups. We introduce an efficient classical framework for computing stabilizer Rényi entropies and stabilizer nullity of generic $N$-qubit wavefunctions. The method combines the fast Walsh-Hadamard transform with an exact partition of Pauli operators, reducing the average cost per sampled Pauli string from $\mathcal{O}(2^N)$ to $\mathcal{O}(N)$. We further develop a Monte Carlo estimator with Clifford preconditioning and find that the required number of samples shows no visible growth with $N$ in our benchmarks. Applying the method to $T$-doped random Clifford circuits, we identify the scrambling ratio $η$ (Clifford gates per $T$ gate) as the key parameter governing magic growth. Each $T$ gate approaches its dilute-limit nonstabilizerness power with only modest Clifford scrambling. Our approach enables quantitative studies of magic in highly entangled states and long-time nonequilibrium dynamics.

quant-ph↗

arXiv2026

Non-Hermitian Disordered Systems

Non-Hermitian disordered systems have emerged as a central arena in modern physics, with ramifications spanning condensed matter, quantum, statistical, and high energy contexts. The same principles also underlie phenomena beyond physics, such as network science, complex systems, and biophysics, where dissipation, nonreciprocity, and stochasticity are ubiquitous. Here, we review the physics and mathematics of non-Hermitian disordered systems, with particular emphasis on non-Hermitian random matrix theory. We begin by presenting the 38-fold symmetry classification of non-Hermitian systems, contrasting it with the 10-fold way for Hermitian systems. After introducing the classic Ginibre ensembles of non-Hermitian random matrices, we survey various diagnostics for complex-spectral statistics and distinct universality classes realized by symmetry. As a key application to physics, we discuss how non-Hermitian random matrix theory characterizes chaos and integrability in open quantum systems. We then turn to the criticality due to the interplay of disorder and non-Hermiticity, including Anderson transitions in the Hatano-Nelson model and its higher-dimensional extensions. We also discuss the effective field theory description of non-Hermitian disordered systems in terms of nonlinear sigma models.

cond-mat.mes-hall↗

arXiv2026

Gauge theory and mixed state criticality

In mixed quantum states, the notion of symmetry is divided into two types: strong and weak symmetry. While spontaneous symmetry breaking (SSB) for a weak symmetry is detected by two-point correlation functions, SSB for a strong symmetry is characterized by the Renyi-2 correlators. In this work, we present a way to construct various SSB phases for strong symmetries, starting from the ground state phase diagram of lattice gauge theory models. In addition to introducing a new type of mixed-state topological phases, we provide models of the criticalities between them, including those with gapless symmetry-protected topological order. We clarify that the ground states of lattice gauge theories are purified states of the corresponding mixed SSB states. Our construction can be applied to any finite gauge theory and offers a framework to study quantum operations between mixed quantum phases.

cond-mat.str-el↗