# Emergent eigenstate solution and emergent Gibbs ensemble for expansion dynamics in optical lattices

## TL;DR

This paper demonstrates that the emergent eigenstate solution applies to the expansion dynamics of Tonks-Girardeau gases in optical lattices after geometric quenches, allowing a description via emergent Hamiltonians and Gibbs ensembles.

## Contribution

It extends the emergent eigenstate solution to geometric quenches in optical lattices and introduces an emergent Gibbs ensemble for finite-temperature initial states.

## Key findings

- Ground states remain in the eigenstate of the emergent Hamiltonian during expansion.
- Finite-temperature states are described by an emergent Gibbs ensemble.
- The approach applies to systems undergoing dynamical fermionization.

## Abstract

Within the emergent eigenstate solution to quantum dynamics [Phys. Rev. X 7, 021012 (2017)], one can construct a local operator (an emergent Hamiltonian) of which the time-evolving state is an eigenstate. Here we show that such a solution exists for the expansion dynamics of Tonks-Girardeau gases in optical lattices after turning off power-law (e.g., harmonic or quartic) confining potentials, which are geometric quenches that do not involve the boost operator. For systems that are initially in the ground state and undergo dynamical fermionization during the expansion, we show that they remain in the ground state of the emergent local Hamiltonian at all times. On the other hand, for systems at nonzero initial temperatures, the expansion dynamics can be described constructing a Gibbs ensemble for the emergent local Hamiltonian (an emergent Gibbs ensemble).