Emergent eigenstate solution for generalized thermalization

TL;DR

This paper introduces an emergent eigenstate framework that constructs local Hamiltonians capturing the entire generalized thermalization process in integrable quantum systems following a quench.

Contribution

It presents a novel emergent eigenstate approach to describe generalized thermalization, linking initial states to eigenstates of emergent Hamiltonians in integrable systems.

Findings

The emergent eigenstate accurately describes the post-quench steady state.

Application to 1D hard-core bosons demonstrates the method's effectiveness.

The approach provides insights into the dynamics of integrable quantum systems.

Abstract

Generalized thermalization is a process that occurs in integrable systems in which unitary dynamics, e.g., following a quantum quench, results in states in which observables after equilibration are described by generalized Gibbs ensembles (GGEs). Here we discuss an emergent eigenstate construction that allows one to built emergent local Hamiltonians of which one eigenstate captures the entire generalized thermalization process following a global quantum quench. Specifically, we study the emergent eigenstate that describes the quantum dynamics of hard-core bosons in one dimension (1D) for which the initial state is a density wave and they evolve under a homogeneous Hamiltonian.