arXiv subjects

Hosho Katsura

Publications and source records attributed to Hosho Katsura.

At least 19 recordsLinked to original sources

arXiv2026

Chiral quantum chaos around exponentially many zero modes in the quantum breakdown model

The quantum breakdown model is a model of randomly interacting fermions, motivated by the physics of dielectric breakdown. Here, we establish classification of symmetry and quantum chaos in a zero-dimensional, all-to-all-interacting version of the quantum breakdown model. It exhibits the $\mathbb{Z}_4$ periodicity with respect to the number of fermionic modes, reminiscent of the symmetry classification of the Sachdev-Ye-Kitaev model. A unique feature of the quantum breakdown model is that it realizes all the five classes with chiral symmetry and hosts an exponentially large number of many-body zero modes protected by the chiral index. We elucidate the separation and scaling of the spectral gap and demonstrate the symmetry-enriched hard-edge spectral statistics as signatures of quantum chaos in the chiral symmetry classes.

cond-mat.str-el↗

arXiv2026

Conserved quantities in a bosonic tight-binding chain with non-Hermitian quartic terms

We investigate local conserved quantities in non-Hermitian bosonic lattice systems whose underlying Yang--Baxter structure remains unclear. Focusing on a one-dimensional bosonic chain with quartic interactions of creation operators, we provide a new representation of the local conserved quantities previously constructed by Sanatani and Shiraishi. Using Fourier transformation and trigonometric identities, we systematically derive these conserved quantities and show directly that they form a mutually commuting family. We further extend the construction to interactions extending beyond a single site, cubic interactions, asymmetric hopping, and an on-site potential. Our results provide a unified framework for constructing and characterizing local conserved quantities in this class of non-Hermitian many-body systems.

cond-mat.stat-mech↗

arXiv2026

Nonlinear Drude weight of the one-dimensional Hubbard model

We investigate nonlinear Drude weights (NLDWs) in the one-dimensional repulsive Hubbard model at zero temperature by combining exact Bethe-ansatz calculations with low-energy effective field theory. At quarter filling, we first derive the strong-coupling expansion of the NLDWs and confirm it numerically over a wide range of interaction strength. We then compare the numerical results with the prediction of the Tomonaga-Luttinger liquid (TLL) description including irrelevant perturbations. While band-curvature corrections yield finite contributions to higher-order NLDWs, the Umklapp interaction predicts divergent NLDWs when the order $n$ of the Drude weight exceeds a threshold determined by the TLL parameter. In contrast, finite-size scaling of the exact Bethe-ansatz results indicates that all calculated NLDWs remain finite in the thermodynamic limit, revealing a discrepancy between the exact results and the predictions of the low-energy effective field theory. At half filling, we analyze the finite-size scaling of the NLDWs across the Mott metal-insulator transition. We derive their asymptotic behavior in the insulating phase and propose a hyperscaling ansatz for NLDWs near the critical point, which is verified numerically. Our results clarify the interaction dependence and critical scaling of nonlinear transport coefficients in the one-dimensional Hubbard model and highlight limitations of the conventional low-energy effective description for higher-order transport.

cond-mat.str-el↗

arXiv2026

Exactly Solvable Disorder-free Quantum Breakdown Model: Spectrum, Thermodynamics, and Dynamics

We introduce and study a disorder-free version of the quantum breakdown model with all-to-all interactions. The Hamiltonian factorizes into the product of the zero-momentum-mode occupation number and a quadratic Hamiltonian including only pairing terms. This structure makes the model exactly solvable and produces an extensive zero-energy degeneracy. We obtain the spectrum and partition function in closed form and analyze the thermodynamics, spectral form factor, two-point functions, and a regulated out-of-time-ordered correlator (OTOC). The OTOC is time independent at leading order in the large-$N$ limit, while its time-dependent contributions first appear at order $1/N$. At infinite temperature, the time-dependent correction reduces to a two-point function arising from the zero-momentum component of the fermion operators. The model therefore provides a controlled setting for isolating the consequences of the breakdown interaction in the absence of disorder, spatial structure, and environmental coupling.

cond-mat.str-el↗

arXiv2026

Exact spectrum and anomalous relaxation in the open disorder-free Sachdev-Ye-Kitaev system

We study a disorder-free variant of the Sachdev-Ye-Kitaev (SYK) model with dissipation within the Gorini-Kossakowski-Sudarshan-Lindblad formalism. By utilizing the integrability of the clean SYK model, we derive an exact solution in a spectrum-resolved form, i.e., the eigenvalues and corresponding projection superoperators of the Liouvillian for arbitrary system size $N$. We determine the scaling of the gap that governs the long-time decay of the two-point correlation functions. Importantly, the gap does not vanish in the dissipationless limit when the thermodynamic limit is taken first, despite the integrability of the model. This phenomenon, known as anomalous relaxation, suggests a possible connection with chaotic dynamics and quantum Ruelle-Pollicott resonances. We also find several spectral features, such as transitions in the Liouvillian spectrum from complex to real eigenvalues with increasing dissipation strength, as well as the convergence of the dissipative form factor to the spectral form factor in the dissipationless limit. These findings indicate that the present model offers a useful platform for exploring nontrivial open dynamics of many-body quantum systems.

cond-mat.str-el↗

arXiv2026

More global randomness from less-random local gates

Random circuits giving rise to unitary designs are key tools in quantum information science and many-body physics. In this work, we investigate a class of random quantum circuits with a specific gate structure. Within this framework, we prove that one-dimensional structured random circuits with non-Haar random local gates can exhibit substantially more global randomness compared to Haar random circuits with the same underlying circuit architecture. In particular, we derive all the exact eigenvalues and eigenvectors of the second-moment operators for these structured random circuits under a solvable condition, by establishing a link to the Kitaev chain, and show that their spectral gaps can exceed those of Haar random circuits. Our findings have applications in improving circuit depth bounds for randomized benchmarking and the generation of approximate unitary 2-designs from shallow random circuits.

quant-ph↗

arXiv2026

Quantum-geometry-driven exact ferromagnetic ground state in a nearly flat band

We construct a Hubbard model with a nearly flat band whose quantum geometry can be tuned independently of the energy dispersion and the Coulomb interaction. We show that, when the nearly flat band is half-filled, the exact ground state of the model exhibits ferromagnetism and that this ferromagnetism is stabilized by the quantum metric through the spin stiffness. Furthermore, we demonstrate that tuning the quantum geometry alone drives a magnetic phase transition. Our nonperturbative results without resorting to mean-field approximations reveal the quantum-geometric origin of ferromagnetism and the underlying many-body physics in dispersive-band systems.

cond-mat.str-el↗

arXiv2026

Exact Quantum Many-Body Scars in 2D Quantum Gauge Models

Quantum many-body scars (QMBS) serve as important examples of ergodicity-breaking phenomena in quantum many-body systems. Despite recent extensive studies, exact QMBS are rare in dimensions higher than one. In this paper, we study a two-dimensional quantum $\mathbb{Z}_2$ gauge model that is dual to a two-dimensional spin-$1/2$ XY model defined on bipartite graphs. We identify the exact eigenstates of the XY model with a tower structure as exact QMBS. Exploiting the duality transformation, we show that the exact QMBS of the XY model (and XXZ model) after the transformation are the exact QMBS of the dual $\mathbb{Z}_2$ gauge model. This construction is versatile and has potential applications for finding new QMBS in other higher-dimensional models.

cond-mat.str-el↗

arXiv2026

Non-equilibirum physics of density-difference dependent Hamiltonian: Quantum Scarring from Emergent Chiral Symmetry

Quantum many-body scars represent a form of weak ergodicity breaking that highlights the unusual physics of thermalization in quantum systems. Understanding scar formation promises insight into the connection between classical statistical mechanics and the quantum world. The existence of quantum many-body scars calls into question how the macroscopic world can arise from the Schrodinger equation. In this work, we demonstrate the existence of quantum many-body scars in the density-difference-dependent Hamiltonian. This Hamiltonian has a particular manifestation of chiral symmetry due to its interaction being neither attractive nor repulsive a prior, but depending on the configuration. As a result of this symmetry and peculiar interaction, we find that this system hosts two different classes of quantum scars; a charge density wave ordered scar and an edge-mode scar. We establish the existence of these scars by examining the entanglement entropy of the system as well as demonstrating robust thermalization breaking time dynamics. For each, we propose simple mechanisms that give rise to these scars which may be applicable to other systems.

cond-mat.quant-gas↗

arXiv2026

Quantum transport on Bethe lattices with non-Hermitian sources and a drain

We consider quantum transport in a tight-binding model on the Bethe lattice of finite generation, which we expect to be the first step toward analyzing electronic transport in a light-harvesting molecule. We seek conditions under which the electronic current from the peripheral light-harvesting sites to the central site reaches its maximum. As a new feature for analyzing quantum transport, we add complex potentials for sources at peripheral sites and a drain at the central site, and solve a non-Hermitian eigenvalue problem, instead of simulating an initial-value problem. Solving the eigenvalue problem clearly reveals which electronic channels contribute most to the quantum transport. The number of eigenstates that can penetrate from the peripheral sites to the central site is quite limited among the total number of eigenstates. All the other eigenstates are localized around the peripheral sites and cannot reach the central site. The former eigenstates can carry current, reducing the problem to quantum transport on a parity-time ($\PT$)-symmetric tight-binding chain. The current has a maximum with respect to the strengths of the sources and the drain. The current decreases as we increase the strengths beyond the maximum and vanishes in the limit of infinite strength. Moreover, the current maximum is given by a zero mode. When the number of links is common to all generations, the current takes the maximum value at the exceptional point where two eigenstates coalesce to a zero mode, which emerges because of the non-Hermiticity due to the $\PT$-symmetric complex potentials. By introducing randomness either into the hopping amplitude or the number of links in each generation of the tree, we obtain a random-hopping tight-binding model, in which the current reaches its maximum not exactly, but approximately, for a zero mode, although it is no longer located at an exceptional point in general.

quant-ph↗

arXiv2026

Towers of Quantum Many-body Scars from Integrable Boundary States

We construct several models with multiple quantum many-body scars (QMBS) using integrable boundary states (IBS). Specifically, we focus on the tilted Néel states, which are parametrized IBS for the spin-1/2 Heisenberg chain, and show that these states can be used to construct a tower of scar states. Our models exhibit periodic revival dynamics, showcasing a characteristic behavior of superpositions of QMBS. Furthermore, the tower of QMBS found in this study possesses a restricted spectrum generating algebra (RSGA) structure, indicating that QMBS are equally spaced in energy. This approach can be extended to two-dimensional models, which can be decomposed into an array of one-dimensional models. In this case, the tilted Néel states again serve as parent states for multiple scar states. These states demonstrate low entanglement entropy, marking them as exact scar states. Notably, their entanglement entropy adheres to the sub-volume law, further solidifying the nonthermal properties of QMBS. Our results provide novel insights into constructing QMBS using IBS, thereby illuminating the connection between QMBS and integrable models.

cond-mat.stat-mech↗

arXiv2026

Dissipative free fermions in disguise

Recently, a class of spin chains known as ``free fermions in disguise'' (FFD) has been discovered, which possess hidden free-fermion spectra even though they are not solvable via the standard Jordan-Wigner transformation. In this work, we extend this FFD framework to open quantum systems governed by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. We establish a general class of exactly solvable open quantum systems within the FFD framework: if the Liouvillian frustration graph is claw-free and has a simplicial clique, the Liouvillian possesses a hidden free-fermion spectrum. In particular, the (even-hole, claw)-free condition automatically guarantees this, enabling exact computation of the Liouvillian gap and an infinite-temperature autocorrelation function. Our results provide the first realization of the FFD mechanism in open quantum systems.

cond-mat.stat-mech↗

arXiv2026

Integrability of a family of clean SYK models from the critical Ising chain

We establish the integrability of a family of Sachdev-Ye-Kitaev (SYK) models with uniform $p$-body interactions. We derive the R-matrix and mutually commuting transfer matrices that generate the Hamiltonians of these models, and obtain their exact eigenspectra and eigenstates. Remarkably, the R-matrix is that of the critical transverse-field Ising chain. This work reveals an unexpected connection between the SYK model, central to many-body quantum chaos, and the critical Ising chain, a cornerstone of statistical mechanics.

cond-mat.stat-mech↗

arXiv2026

Open quantum spin chains with non-reciprocity: a theoretical approach based on the time-dependent generalized Gibbs ensemble

We study an open quantum spin chain with non-reciprocal dissipation using a theoretical approach known as time-dependent generalized Gibbs ensemble. In the regime of weak dissipation the system is fully characterized by its rapidity distribution and we derive a closed set of coupled differential equations governing their time evolution. We check the accuracy of this theory by benchmarking the results against numerical simulations. Using this framework we are able to compute both the magnetization density and current dynamics, identifying some relations between the two. The problem of the anomalous power-law exponents identified in a previous work is discussed. Our work constitutes a theoretical approach that is able to describe the physics of non-reciprocal open quantum spin chains beyond analyses based on non-interacting fermions.

quant-ph↗

arXiv2025

Systematic construction of asymptotic quantum many-body scar states and their relation to supersymmetric quantum mechanics

We develop a systematic method for constructing asymptotic quantum many-body scar (AQMBS) states. While AQMBS states are closely related to quantum many-body scar (QMBS) states, they exhibit key differences. Unlike QMBS states, AQMBS states are not energy eigenstates of the Hamiltonian, making their construction more challenging. We demonstrate that, under appropriate conditions, AQMBS states can be obtained as low-lying gapless excited states of a parent Hamiltonian, which has a QMBS state as its ground state. Furthermore, our formalism reveals a connection between QMBS and supersymmetric (SUSY) quantum mechanics. The QMBS state can be interpreted as a SUSY-unbroken ground state.

cond-mat.stat-mech↗

arXiv2025

$\mathrm{SU}(3)$ Fermi-Hubbard gas with three-body losses: symmetries and dark states

We study an $\mathrm{SU}(3)$ invariant Fermi-Hubbard gas undergoing on-site three-body losses. The model presents eight independent strong symmetries preventing the complete depletion of the gas. By making use of a basis of semi-standard Young tableaux states, we reveal the presence of a rich phenomenology of stationary states. We classify the latter according to the irreducible representation of $\mathrm{SU}(3)$ to which they belong. We finally discuss the presence of three-particle stationary states that are not protected by the $\mathrm{SU}(3)$ symmetry.

cond-mat.quant-gas↗

arXiv2025

A brief note on the G$_2$ Affleck-Kennedy-Lieb-Tasaki chain

We consider the valence bond solid (VBS) state built of singlet pairs of fundamental representations and projected onto adjoint representations of the exceptional Lie group G$_2$. The two-point correlation function in the VBS state is non-vanishing only for nearest neighbours, but possesses finite string order. We construct a parent Hamiltonian for the VBS state, which constitutes the G$_2$ analog of the famous AKLT chain.

cond-mat.str-el↗

arXiv2025

Edge-Edge Correlations without Edge-States: $η$-clustering State as Ground State of the Extended Attractive SU(3) Hubbard Chain

We explore the phase diagram of the extended attractive SU($3$) Hubbard chain with two-body hopping and nearest-neighbor attraction at half-filling. In the large on-site attraction limit, we identify three different phases: phase separation (PS), Tomonaga-Luttinger liquid (TLL), and charge density wave (CDW). Our analysis reveals that the $η$-clustering state, a three-component generalization of the $η$-pairing state, becomes the ground state at the boundary between the PS and TLL phases. On an open chain, this state exhibits an edge-edge correlation, which we call boundary off-diagonal long-range order (bODLRO). Using the density matrix renormalization group (DMRG) method, we numerically study the phase diagram of the model with large but finite on-site interactions and find that the numerical results align with those obtained in the strong coupling limit.

cond-mat.str-el↗