arXiv subjects

Yasushi Yoneta

Publications and source records attributed to Yasushi Yoneta.

10 recordsLinked to original sources

arXiv2026

Second law of thermodynamics in closed quantum many-body systems

The second law of thermodynamics for adiabatic operations -- constraints on state transitions in closed systems under external control -- is one of the fundamental principles of thermodynamics. On the other hand, it is recently established that even pure quantum states can represent thermal equilibrium. However, pure quantum states do not satisfy the second law in that they are not passive, i.e., work can be extracted from them if arbitrary unitary operations are allowed. It therefore remains unresolved how quantum mechanics can be reconciled with thermodynamics. Here, based on our key quantum-mechanical notions of thermal equilibrium and adiabatic operations, we address the emergence of the second law for adiabatic operations in the thermodynamics limit. We first introduce infinite-observable macroscopic thermal equilibrium (iMATE); a quantum state, including pure states, is in iMATE if the expectation values of all additive observables agree with their equilibrium values. We also introduce a macroscopic operation as unitary evolution generated by a time-dependent additive Hamiltonian, which is regarded as corresponding to adiabatic operations. Employing these concepts, we show that no extensive work can be extracted from any quantum state in iMATE through any macroscopic operations. Furthermore, we introduce a quantum-mechanical form of entropy density such that it agrees with thermodynamic entropy density for any quantum state in iMATE. We then prove that for any initial state in iMATE, this entropy density cannot be decreased by any macroscopic operations, followed by a time-independent relaxation process. Our theory thus proves two different forms of the second law, by adopting macroscopically reasonable classes of observables, equilibrium states, and operations. We also discuss the time scales of macroscopic operations in these results.

cond-mat.stat-mech↗

arXiv2026

Crosscap Quenches and Entanglement Evolution

Understanding the mechanisms by which complex correlations emerge through the dynamics of quantum many-body systems remains a fundamental challenge in modern physics. To address this, quench dynamics starting from nonthermal states have been extensively studied, leading to significant progress. In this paper, we propose a novel quench protocol, termed the "crosscap quench", to investigate how highly structured thermal pure states relax into typical ones. We begin by analyzing conformal field theories (CFTs) and derive universal features in the time evolution of the entanglement entropy. Furthermore, leveraging the AdS/CFT correspondence, we study holographic CFTs, providing an analytically tractable example in chaotic CFTs. Finally, we validate these findings through numerical simulations in both nonintegrable and integrable quantum spin systems.

hep-th↗

arXiv2025

Optimal statistical ensembles for quantum thermal state preparation within the quantum singular value transformation framework

Preparing thermal equilibrium states is an essential task for finite-temperature quantum simulations. In statistical mechanics, microstates in thermal equilibrium can be obtained from statistical ensembles. To date, numerous ensembles have been devised, ranging from Gibbs ensembles such as the canonical and microcanonical ensembles to a variety of generalized ensembles. Since these ensembles yield equivalent thermodynamic predictions, one can freely choose an ensemble for computational convenience. In this paper, we exploit this flexibility to develop an efficient quantum algorithm for preparing thermal equilibrium states. We first present a quantum algorithm for implementing generalized ensembles within the framework of quantum singular value transformation. We then perform a detailed analysis of the computational cost and elucidate its dependence on the choice of the ensemble. Our analysis shows that employing an appropriate ensemble can significantly mitigate ensemble-dependent overhead and yield improved scaling of the computational cost with system size compared to existing methods based on the canonical ensemble. We also numerically demonstrate that our approach achieves a significant reduction in the computational cost even for small finite-size systems. Our algorithm applies to arbitrary thermodynamic systems at any temperature and is thus expected to offer a practical and versatile method for computing finite-temperature properties of quantum many-body systems. These results highlight the potential of ensemble design as a powerful tool for enhancing the efficiency of a broad class of quantum algorithms.

quant-ph↗

arXiv2024

Thermal Pure States for Systems with Antiunitary Symmetries and Their Tensor Network Representations

Thermal pure state algorithms, which employ pure quantum states representing thermal equilibrium states instead of statistical ensembles, are useful both for numerical simulations and for theoretical analysis of thermal states. However, their inherently large entanglement makes it difficult to represent efficiently and limits their use in analyzing large systems. Here, we propose a new tensor network algorithm for constructing thermal pure states for systems with certain antiunitary symmetries, such as time-reversal or complex conjugate symmetry. Our method utilizes thermal pure states that, while exhibiting volume-law entanglement, can be mapped to tensor network states through simple transformations. Furthermore, our approach does not rely on random sampling and thus avoids statistical uncertainty. Moreover, we can compute not only thermal expectation values of local observables but also thermodynamic quantities. We demonstrate the validity and utility of our method by applying it to the one-dimensional XY model and the two-dimensional Ising model on a triangular lattice. Our results suggest a new class of variational wave functions for volume-law states that are not limited to thermal equilibrium states.

cond-mat.stat-mech↗

arXiv2024

Exact Thermal Eigenstates of Nonintegrable Spin Chains at Infinite Temperature

The eigenstate thermalization hypothesis (ETH) plays a major role in explaining thermalization of isolated quantum many-body systems. However, there has been no proof of the ETH in realistic systems due to the difficulty in the theoretical treatment of thermal energy eigenstates of nonintegrable systems. Here, we write down analytically thermal eigenstates of nonintegrable spin chains. We consider a class of theoretically tractable volume-law states, which we call entangled antipodal pair (EAP) states. These states are thermal, in the most fundamental sense that they are indistinguishable from the Gibbs state with respect to all local observables, with infinite temperature. We then identify Hamiltonians having the EAP state as an eigenstate and rigorously show that some of these Hamiltonians are nonintegrable. Furthermore, a thermal pure state at an arbitrary temperature is obtained by the imaginary time evolution of an EAP state. Our results offer a potential avenue for providing a provable example of the ETH.

cond-mat.stat-mech↗

arXiv2024

Counting atypical black hole microstates from entanglement wedges

Disentangled black hole microstates are atypical states in holographic CFTs whose gravity duals do not have smooth horizons. If there exist sufficiently many disentangled microstates to account for the entire black hole entropy, then any black hole microstate can be written as a superposition of states without smooth horizons. We show that there exist sufficiently many disentangled microstates to account for almost the entire black hole entropy of a large AdS black hole at the semiclassical limit $G_N\rightarrow 0$. In addition, we also argue that in generic quantum many-body systems with short-ranged interactions, there exist sufficiently many area law states in the microcanonical subspace to account for almost the entire thermodynamic entropy in the standard thermodynamic limit. Area law states are atypical since a typical state should contain volume law entanglement. Furthermore, we also present an explicit way to construct such a set of area law states, and argue that the same construction may also be used to construct disentangled states.

hep-th↗

arXiv2024

Efficient Simulation of Low Temperature Physics in One-Dimensional Gapless Systems

We discuss the computational efficiency of the finite temperature simulation with the minimally entangled typical thermal states (METTS). To argue that METTS can be efficiently represented as matrix product states, we present an analytic upper bound for the average entanglement Renyi entropy of METTS for Renyi index $0<q\leq 1$. In particular, for 1D gapless systems described by CFTs, the upper bound scales as $\mathcal{O}(c N^0 \log β)$ where $c$ is the central charge and $N$ is the system size. Furthermore, we numerically find that the average Renyi entropy exhibits a universal behavior characterized by the central charge and is roughly given by half of the analytic upper bound. Based on these results, we show that METTS provide a significant speedup compared to employing the purification method to analyze thermal equilibrium states at low temperatures in 1D gapless systems.

cond-mat.stat-mech↗

arXiv2023

Statistical ensembles for phase coexistence states specified by noncommutative additive observables

A phase coexistence state cannot be specified uniquely by any intensive parameters, such as the temperature and the magnetic field, because they take the same values over all coexisting phases. It can be specified uniquely only by an appropriate set of additive observables. Hence, to analyze phase coexistence states the statistical ensembles that are specified by additive observables have been employed, such as the microcanonical and restricted ensembles. However, such ensembles are ill-defined or ill-behaved when some of the additive observables do not commute with each other. Here, we solve this fundamental problem by extending a generalized ensemble in such a way that it is applicable to phase coexistence states which are specified by noncommutative additive observables. We prove that this ensemble correctly gives the density matrix corresponding to phase coexistence states of general quantum systems as well as the thermodynamic functions. Furthermore, these ensembles are convenient for practical calculations because of good analytic properties and useful formulas by which temperature and other intensive parameters are directly obtained from the expectation values of the additive observables. As a demonstration, we apply our formulation to a two-dimensional system whose phase coexistence states are specified by an additive observable (order parameter) that does not commute with the Hamiltonian.

cond-mat.stat-mech↗

arXiv2023

Stationarity of quantum statistical ensembles at first-order phase transition points

We study the dynamics of quantum statistical ensembles at first-order phase transition points of finite macroscopic systems. First, we show that at the first-order phase transition point of systems with an order parameter that does not commute with the Hamiltonian, any quantum state with a non-zero value of the order parameter always evolves towards a macroscopically distinct state after a sufficiently long time. From this result, we argue that stationarity required for statistical ensembles should be interpreted as stationarity on a sufficiently long but finite time scale. Finally, we prove that the density matrix of the squeezed ensemble, a class of generalized statistical ensembles proposed as the only concrete method of constructing phase coexistence states applicable to general quantum systems, is locally stationary on time scales diverging in the thermodynamic limit. Our results support the validity of the squeezed ensemble from a dynamical point of view and open the door to non-equilibrium statistical physics at the first-order phase transition point.

cond-mat.stat-mech↗

arXiv2019

Squeezed ensemble for systems with first-order phase transitions

All ensembles of statistical mechanics are equivalent in the sense that they give the equivalent thermodynamic functions in the thermodynamic limit. However, when investigating microscopic structures in the first-order phase transition region, one must choose an appropriate statistical ensemble. The appropriate choice is particularly important when one investigates finite systems, for which even the equivalence of ensembles does not hold. We propose a class of statistical ensembles, which always give the correct equilibrium state even in the first-order phase transition region. We derive various formulas for this class of ensembles, including the one by which temperature is obtained directly from energy without knowing entropy. Moreover, these ensembles are convenient for practical calculations because of good analytic properties. We also derive formulas which relate statistical-mechanical quantities of different ensembles, including the conventional ones, for finite systems. The formulas are useful for obtaining results with smaller finite-size effects, and for improving the computational efficiency. The advantages of the squeezed ensembles are confirmed by applying them to the Heisenberg model and the frustrated Ising model.

cond-mat.stat-mech↗