Abstract
The eigenstate thermalization hypothesis (ETH) is a successful theory that provides sufficient criteria for ergodicity in quantum many-body systems. Most studies were carried out for Hamiltonians relevant for ultracold quantum gases and single-component systems of spins, fermions, or bosons. The paradigmatic example for thermalization in solid-state physics are phonons serving as a bath for electrons. This situation is often viewed from an open-quantum system perspective. Here, we ask whether a minimal microscopic model for electron-phonon coupling is quantum chaotic and whether it obeys ETH, if viewed as a closed quantum system. Using exact diagonalization, we address this question in the framework of the Holstein polaron model. Even though the model describes only a single itinerant electron, whose coupling to dispersionless phonons is the only integrability-breaking term, we find that the spectral statistics and the structure of Hamiltonian eigenstates exhibit essential properties of the corresponding random-matrix ensemble. Moreover, we verify the ETH ansatz both for diagonal and offdiagonal matrix elements of typical phonon and electron observables, and show that the ratio of their variances equals the value predicted from random-matrix theory.
Highlights
Understanding whether and how an isolated quantum many-body system approaches thermal equilibrium after being driven far from equilibrium has been a tremendous theoretical challenge since the birth of quantum mechanics [1,2]
An additional impetus to the theoretical community was given by the work of Rigol et al [16] who demonstrated that the eigenstate thermalization hypothesis (ETH), pioneered by Deutsch [17] and Srednicki [18], provides a relevant framework to describe statistical properties of eigenstates of lattice Hamiltonians, applicable to ongoing experiments with ultracold atoms on optical lattices [7,13,14]
We addressed the question whether the hallmark features of the ETH can be observed in a paradigmatic condensed matter model that includes both electron and phonon degrees of freedom
Summary
Understanding whether and how an isolated quantum many-body system approaches thermal equilibrium after being driven far from equilibrium has been a tremendous theoretical challenge since the birth of quantum mechanics [1,2]. The ETH has been verified for a wide number of lattice models such as nonintegrable spin-1/2 chains [23,24,25,26,27,28,29,30,31,32,33], ladders [26,34,35,36], and square lattices [37,38,39], interacting spinless fermions [40,41], Bose-Hubbard [26,42], and FermiHubbard chains [43], dipolar hard-core bosons [44], quantum dimer models [45], and Fibonacci anyons [46] In these examples, mostly, direct two-body interactions in systems of either spins, fermions, or bosons are responsible for rendering the system ergodic.
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