# Quantum dynamics of impenetrable SU(N) fermions in one-dimensional lattices

## TL;DR

This paper investigates the quantum quench dynamics of strongly interacting SU(N) fermions in one-dimensional lattices, revealing emergent correlations and distributions during expansion, and establishing a framework for analyzing their equilibration.

## Contribution

It introduces an exact approach to study SU(N) fermion dynamics, uncovering phenomena like Gaussian correlations and quasimomentum to rapidity distribution transformation, and discusses equilibration via a generalized Gibbs ensemble.

## Key findings

- Gaussian one-body correlations emerge during domain wall melting.
- Quasimomentum distribution transforms into rapidity distribution over time.
- Observables after equilibration are described by a generalized Gibbs ensemble.

## Abstract

We study quantum quench dynamics in the Fermi-Hubbard model, and its SU($N$) generalizations, in one-dimensional lattices in the limit of infinite onsite repulsion between all flavors. We consider families of initial states with generalized Neel order, namely, initial state in which there is a periodic $N$-spin pattern with consecutive fermions carrying distinct spin flavors. We introduce an exact approach to describe the quantum evolution of those systems, and study two unique transient phenomena that occur during expansion dynamics in finite lattices. The first one is the dynamical emergence of Gaussian one-body correlations during the melting of sharp (generalized) Neel domain walls. Those correlations resemble the ones in the ground state of the SU($N$) model constrained to the same spin configurations. This is explained using an emergent eigenstate solution to the quantum dynamics. The second phenomenon is the transformation of the quasimomentum distribution of the expanding strongly interacting SU($N$) gas into the rapidity distribution after long times. Finally, we study equilibration in SU($N$) gasses and show that observables after equilibration are described by a generalized Gibbs ensemble. Our approach can be used to benchmark analytical and numerical calculations of dynamics of strongly correlated SU($N$) fermions at large $U$.