Relaxation of a one-dimensional Mott insulator after an interaction quench

TL;DR

This paper derives the exact time evolution of a one-dimensional integrable fermionic Hubbard model after a sudden interaction change, showing it relaxes to a steady state described by a generalized Gibbs ensemble, regardless of initial state being metallic or Mott-insulating.

Contribution

It provides an exact solution for the dynamics of the 1/r Hubbard model post-quench and clarifies conditions under which generalized Gibbs ensembles accurately describe steady states.

Findings

The system relaxes to a steady state after a quench.

The Mott gap does not prevent relaxation.

Generalized Gibbs ensembles correctly predict steady state properties under certain conditions.

Abstract

We obtain the exact time evolution for the one-dimensional integrable fermionic 1/r Hubbard model after a sudden change of its interaction parameter, starting from either a metallic or a Mott-insulating eigenstate. In all cases the system relaxes to a new steady state, showing that the presence of the Mott gap does not inhibit relaxation. The properties of the final state are described by a generalized Gibbs ensemble. We discuss under which conditions such ensembles provide the correct statistical description of isolated integrable systems in general. We find that generalized Gibbs ensembles do predict the properties of the steady state correctly, provided that the observables or initial states are sufficiently uncorrelated in terms of the constants of motion.