Integrable quenches in the Hubbard model

TL;DR

This paper analyzes the quench dynamics of the 1D Hubbard model using the Quench Action formalism, introducing integrable initial states with exact overlap calculations, revealing stationary behaviors and entanglement features.

Contribution

It provides an exact characterization of the late-time regime for a class of integrable initial states in the Hubbard model, including explicit overlap formulas and entanglement dynamics.

Findings

Exact overlaps between initial states and Bethe eigenstates are derived.

Stationary local observables, like double occupancy, are explicitly computed.

Entanglement entropy shows a double-slope structure at intermediate interactions.

Abstract

We study the quench dynamics of the one-dimensional Hubbard model through the Quench Action formalism. We introduce a class of integrable initial states -- expressed as product states over two sites -- for which we can provide an exact characterisation of the late-time regime. This is achieved by finding a closed-form expression for the overlaps between our states and the Bethe ansatz eigenstates, which we check explicitly in the limits of low densities and infinite repulsion. Our solution gives access to the stationary values attained by local observables (we show the explicit example of the density of doubly occupied sites) and the asymptotic entanglement dynamics directly in the thermodynamic limit. Interestingly, we find that for intermediate interaction strength R\'enyi entropies display a double-slope structure.