Emergent eigenstate solution to quantum dynamics far from equilibrium

TL;DR

This paper introduces a new class of nonequilibrium eigenstates governed by an emergent local Hamiltonian, enabling the analysis of quantum dynamics far from equilibrium in many-body systems.

Contribution

It presents the concept of emergent eigenstates and local Hamiltonians, providing a novel framework for understanding quantum dynamics in non-equilibrium states.

Findings

Current-carrying states can be ground states of emergent local Hamiltonians.

Time-evolving states can be highly excited eigenstates with non-volume-law entanglement.

Emergent eigenstates allow extensive-time analysis of quantum transport and expansion.

Abstract

The quantum dynamics of interacting many-body systems has become a unique venue for the realization of novel states of matter. Here we unveil a new class of nonequilibrium states that are eigenstates of an emergent local Hamiltonian. The latter is explicitly time dependent and, even though it does not commute with the physical Hamiltonian, it behaves as a conserved quantity of the time-evolving system. We discuss two examples in which the emergent eigenstate solution can be applied for an extensive (in system size) time: transport in one-dimensional lattices with initial particle (or spin) imbalance, and sudden expansion of quantum gases in optical lattices. We focus on noninteracting spinless fermions, hard-core bosons, and the Heisenberg model. We show that current-carrying states can be ground states of emergent local Hamiltonians, and that they can exhibit a quasimomentum distribution function that is peaked at nonzero (and tunable) quasimomentum. We also show that time-evolving states can be highly-excited eigenstates of emergent local Hamiltonians, with an entanglement entropy that does not exhibit volume-law scaling.