Preferred basis derived from eigenstate thermalization hypothesis

TL;DR

This paper investigates how the eigenstate thermalization hypothesis influences the long-time behavior of a central quantum system's reduced density matrix, revealing a preferred basis derived from the system-environment interaction.

Contribution

It introduces a theoretical framework linking ETH to the emergence of a preferred basis in open quantum systems, supported by analytical derivations and numerical simulations.

Findings

Derivation of relations among RDM elements under ETH conditions

Identification of a preferred basis from a renormalized Hamiltonian

Numerical confirmation using a qubit coupled to an Ising chain

Abstract

We study the long-time average of the reduced density matrix (RDM) of an $m$-level central system, which is locally coupled to a large environment, under an overall Schr\"{o}dinger evolution of the total system. We consider a class of interaction Hamiltonian, whose environmental part satisfies the so-called eigenstate thermalization hypothesis (ETH) ansatz with a constant diagonal part in the energy region concerned. On the eigenbasis of the central system's Hamiltonian, $\frac{1}{2}(m-1)(m+2)$ relations among elements of the averaged RDM are derived. When steady states exist, these relations imply the existence of a preferred basis, given by a renormalized Hamiltonian that includes certain averaged impact of the system-environment interaction. Numerical simulations performed for a qubit coupled to a defect Ising chain conform the analytical predictions.