Does the eigenstate thermalization hypothesis hold for non-local operators?

Vanja Dunjko, Maxim Olshanii

Nima Lashkari, Anatoly Y. Dymarsky, Hong Liu

Abstract We investigate the eigenstate thermalization hypothesis (ETH) in d + 1 dimensional conformal field theories by studying the reduced density matrices in energy eigenstates. We show that if the local probes of the finitely excited primary eigenstates satisfy ETH, then any finite energy observable with support on a subsystem of finite size satisfies ETH. In two dimensions, we discover that if ETH holds locally, the finite size reduced density matrix of states created by heavy primary operators is well-approximated by a projection to the Virasoro identity block.

Anushya Chandran, Marc Daniel Schulz, F. J. Burnell

Many phases of matter, including superconductors, fractional quantum Hall fluids, and spin liquids, are described by gauge theories with constrained Hilbert spaces. However, thermalization and the applicability of quantum statistical mechanics has primarily been studied in unconstrained Hilbert spaces. In this paper, we investigate whether constrained Hilbert spaces permit local thermalization. Specifically, we explore whether the eigenstate thermalization hypothesis (ETH) holds in a pinned Fibonacci anyon chain, which serves as a representative case study. We first establish that the constrained Hilbert space admits a notion of locality by showing that the influence of a measurement decays exponentially in space. This suggests that the constraints are no impediment to thermalization. We then provide numerical evidence that ETH holds for the diagonal and off-diagonal matrix elements of various local observables in a generic disorder-free nonintegrable model. We also find that certain nonlocal observables obey ETH.

Xiao 晓 Wang 王, Wen-ge Wang

Maxim Olshanii

Giorgio Cipolloni, Jonah Kudler-Flam

The eigenstate thermalization hypothesis (ETH) represents a cornerstone in the theoretical understanding of the emergence of thermal behavior in closed quantum systems. Here, the authors investigate to what extent the ETH holds for non-Hermitian Hamiltonians, relevant for open and monitored quantum systems, and come to the surprising conclusion that fluctuations are greatly enhanced, indicating the breakdown of thermalization.