Eigenstate Thermalization Hypothesis and Quantum Thermodynamics

Vanja Dunjko, Maxim Olshanii

Chaitanya Murthy, Arman Babakhani, Fernando Iniguez +2 more

The eigenstate thermalization hypothesis (ETH) explains why nonintegrable quantum many-body systems thermalize internally if the Hamiltonian lacks symmetries. If the Hamiltonian conserves one quantity ("charge"), the ETH implies thermalization within a charge sector-in a microcanonical subspace. But quantum systems can have charges that fail to commute with each other and so share no eigenbasis; microcanonical subspaces may not exist. Furthermore, the Hamiltonian will have degeneracies, so the ETH need not imply thermalization. We adapt the ETH to noncommuting charges by positing a non-Abelian ETH and invoking the approximate microcanonical subspace introduced in quantum thermodynamics. Illustrating with SU(2) symmetry, we apply the non-Abelian ETH in calculating local operators' time-averaged and thermal expectation values. In many cases, we prove, the time average thermalizes. However, we find cases in which, under a physically reasonable assumption, the time average converges to the thermal average unusually slowly as a function of the global-system size. This work extends the ETH, a cornerstone of many-body physics, to noncommuting charges, recently a subject of intense activity in quantum thermodynamics.

Matthew P. A. Fisher, Tarun Grover

Takaaki Monnai

The eigenstate thermalization hypothesis (ETH) states that for nonintegrable systems, each energy eigenstate accurately gives microcanonical expectation values for a class of observables. In this paper, we explore the ETH in terms of the time-energy uncertainty and an intrinsic thermal nature shared by the majority of quasi eigenstates of operationally defined 'time operator': First, we show that the energy eigenstates are superposition of uncountably many quasi eigenstates of suitably defined 'time operator'. Majority of such quasi eigenstates are thermal for thermodynamic isolated quantum many-body systems and approximately orthogonal in terms of extremely short relaxation time of the fidelity. In this manner, our scenario provides a theoretical explanation of ETH.

Van A. Ngo, Stephan Haas

Aleksander Lasek, Jae Dong Noh, Jade LeSchack +1 more

The eigenstate thermalization hypothesis (ETH) explains how generic quantum many-body systems thermalize internally. It implies that local operators' time-averaged expectation values approximately equal their thermal expectation values, regardless of microscopic details. The ETH's range of applicability therefore impacts theory and experiments. Murthy et al. [Phys. Rev. Lett. 130, 140402 (2023)0031-900710.1103/PhysRevLett.130.140402] recently showed that non-Abelian symmetries conflict with the ETH. Such symmetries have excited interest in quantum thermodynamics lately, as they are equivalent to conserved quantities that fail to commute with each other and noncommutation is a quintessentially quantum phenomenon. Murthy et al. proposed a non-Abelian ETH, which we support numerically. The numerics model a one-dimensional next-nearest-neighbor Heisenberg chain of 18 qubits. We represent local operators with matrices relative to an energy eigenbasis. The matrices bear out seven predictions of the non-Abelian ETH. We also prove analytically that the non-Abelian ETH exhibits a self-consistency property. The proof relies on a thermodynamic-entropy definition different from that of Murthy et al. This work initiates the observation and application of the non-Abelian ETH.