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Hironobu Yoshida

Publications and source records attributed to Hironobu Yoshida.

13 recordsLinked to original sources
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

Superconductivity and Low Energy Excitations in an Attractive Hubbard Model

We study an attractive Hubbard model on bipartite lattices. In the grand canonical formalism,we prove the existence of superconducting long-range order in the ground state on Lieb lattices with the chemical potential corresponding to half filling. We also study the low-energy excitations above several ground states for the translationally invariant Hamiltonian. We prove the following: (i) The pairing excitations are gapless above the ground states when the number of fermions deviates from that of the half filling by the order of the volume. (ii) A certain class of single-fermion excitations shows a non-vanishing spectral gap above the ground state with an even number of fermions in a strong coupling and low-density regime.

math-ph↗
arXiv2026

Theory of Steady States for Lindblad Equations beyond Time-Independence: Classification, Uniqueness and Symmetry

We present a rigorous and comprehensive classification of the asymptotic behavior of time-dependent Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equations under the assumption of Hermitian jump operators. Our results apply to a broad class of GKSL equations whose time dependence is assumed to be recurrent, including time-independent, periodic, quasiperiodic, and certain classes of random time dependence. Our main contributions are twofold: first, we establish a criterion for the uniqueness of steady states. The criterion is formulated in terms of the algebra generated by the GKSL generators and provides a necessary and sufficient condition when the generators are analytic functions of time. We demonstrate the utility of our criterion through prototypical examples, including quantum many-body spin chains. Second, we extend the concept of strong symmetry for time-dependent GKSL equations by introducing two distinct forms, strong symmetry in the Schrödinger picture and that in the interaction picture, and completely classify the asymptotic dynamics with them. More concretely, we rigorously uncover that the strong symmetry in the interaction picture is responsible for non-trivial time-dependent steady states, such as coherent oscillations, whereas that in the Schrödinger picture controls the existence of time-independent steady states. This classification not only encompasses established mechanisms underlying non-trivial oscillatory steady states, such as strong dynamical symmetry and Floquet dynamical symmetry, but also reveals symmetry-predicted, time-dependent asymptotic dynamics in a novel class of open quantum systems. Our framework thus provides a rigorous foundation for controlling dissipative quantum systems in a time-dependent manner.

quant-ph↗
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

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

Asymptotically optimal unitary estimation in $\mathrm{SU}(3)$ by the analysis of graph Laplacian

Unitary estimation is the task to estimate an unknown unitary operator $U\in\mathrm{SU}(d)$ with $n$ queries to the corresponding unitary operation, and its accuracy is evaluated by an estimation fidelity. We show that the optimal asymptotic fidelity of $3$-dimensional unitary estimation is given by $F_\mathrm{est}(n,d=3) = 1-\frac{56π^2}{9n^2} + O(n^{-3})$ by the analysis of the graph Laplacian based on the finite element method. We also show the lower bound on the fidelity of $d$-dimensional unitary estimation for an arbitrary $d$ given by $F_\mathrm{est}(n,d) \geq 1- \frac{(d+1)(d-1)(3d-2)(3d-1)}{6n^2} + O(n^{-3})$ achieving the best known lower bound and tight scaling with respect to $n$ and $d$. This lower bound is derived based on the unitary estimation protocol shown in [J. Kahn, Phys. Rev. A 75, 022326, 2007].

quant-ph↗
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↗
arXiv2024

Universality and two-body losses: lessons from the effective non-Hermitian dynamics of two particles

We study the late-time dynamics of two particles confined in one spatial dimension and subject to two-body losses. The dynamics is exactly described by a non-Hermitian Hamiltonian that can be analytically studied both in the continuum and on a lattice. The asymptotic decay rate and the universal power-law form of the decay of the number of particles are exactly computed in the whole parameter space of the problem. When in the initial state the two particles are far apart, the average number of particles in the setup decays with time $t$ as $t^{-1/2}$; a different power law, $t^{-3/2}$, is found when the two particles overlap in the initial state. These results are valid both in the continuum and on a lattice, but in the latter case a logarithmic correction appears.

cond-mat.quant-gas↗
arXiv2023

Jordan Decomposition of Non-Hermitian Fermionic Quadratic Forms

We give a rigorous proof of Conjecture 3.1 by Prosen [Prosen T 2010 J. Stat. Mech. $\textbf{2010}$ P07020] on the nilpotent part of the Jordan decomposition of a quadratic fermionic Liouvillian. We also show that the number of the Jordan blocks of each size can be expressed in terms of the coefficients of a polynomial called the $q$-binomial coefficient and describe the procedure to obtain the Jordan canonical form of the nilpotent part.

quant-ph↗
arXiv2023

Liouvillian gap and single spin-flip dynamics in the dissipative Fermi-Hubbard model

Motivated by recent progress in cold-atom experiments, we analyze the SU($N$) Fermi-Hubbard model on a $d$-dimensional hypercubic lattice with two-body loss. By focusing on states near the ferromagnetic steady states, we obtain the Liouvillian gap in closed form for any $d$ and $N$. We also investigate the dynamics of a ferromagnetic initial state with a single spin flip both analytically and numerically. In particular, we show that, by decreasing the strength of the interaction and loss, the survival probability of the spin flip exhibits a crossover from the power-law decay to the exponential decay. We expect that our findings can be tested experimentally with ultracold alkaline-earth-like atoms in an optical lattice.

cond-mat.quant-gas↗
arXiv2022

Exact eigenstates of extended SU($N$) Hubbard models: Generalizations of $η$-pairing states with $N$-particle off-diagonal long-range order

We consider $N$-particle generalizations of $η$-pairing states in a chain of $N$-component fermions and show that these states are exact (high-energy) eigenstates of an extended SU($N$) Hubbard model. We compute the singlet correlation function of the states and find that its behavior is qualitatively different for even and odd $N$. When $N$ is even, these states exhibit off-diagonal long-range order in $N$-particle reduced density matrix. On the other hand, when $N$ is odd, the correlations decay exponentially with distance in the bulk, but end-to-end correlations do not vanish in the thermodynamic limit. Finally, we prove that these states are the unique ground states of suitably tailored Hamiltonians.

cond-mat.str-el↗
arXiv2021

Rigorous results on the ground state of the attractive SU($N$) Hubbard model

We study the attractive SU($N$) Hubbard model with particle-hole symmetry. The model is defined on a bipartite lattice with the number of sites $N_A$ $(N_B)$ in the $A$ $(B)$ sublattice. We prove three theorems that allow us to identify the basic ground-state properties: the degeneracy, the fermion number, and the SU($N$) quantum number. We also show that the ground state exhibits charge density wave order when $|N_A-N_B|$ is macroscopically large. The theorems hold for a bipartite lattice in any dimension, even without translation invariance.

cond-mat.str-el↗