Basis dependence of eigenstate thermalization

TL;DR

This paper investigates how the eigenstate thermalization hypothesis depends on the choice of basis in systems with degeneracies, revealing basis-dependent violations and implications for thermalization and relaxation.

Contribution

It demonstrates basis dependence of eigenstate thermalization in degenerate systems, proves degeneracies arise from symmetries, and provides bounds on basis effects.

Findings

Eigenstate thermalization can vanish or hold depending on basis choice.

Degeneracies are linked to spatial symmetries like translation and reflection.

Basis choice influences thermalization and relaxation properties.

Abstract

Eigenstate thermalization refers to the property that an energy eigenstate of a many-body system is indistinguishable from a thermal equilibrium ensemble at the same energy as far as expectation values of local observables are concerned. In systems with degeneracies, the choice of an energy eigenbasis is not unique and the fraction of basis states exhibiting eigenstate thermalization can vary. We present a simple example where this fraction vanishes in the thermodynamic limit for one basis choice, but remains nonzero for another choice. In other words, the weak eigenstate thermalization hypothesis is satisfied in the first, but violated in the second basis. We furthermore prove that degeneracies must abound whenever a system is simultaneously symmetric under spatial translations and reflection. Finally, we derive general bounds on how strongly eigenstate thermalization may depend on the choice of the basis, and we reveal some interesting implications regarding the temporal relaxation properties of such systems.