Bethe Ansatz approach to quench dynamics in the Richardson model

TL;DR

This paper introduces a nearly exact, integrability-based numerical method to analyze long-time non-equilibrium dynamics after a quantum quench in the Richardson model, overcoming previous computational limitations.

Contribution

It develops a controlled, non-perturbative approach using algebraic Bethe ansatz to study quench dynamics in an integrable fermionic pairing model, enabling large system analysis.

Findings

The method provides controlled access to long-time dynamics.

Hilbert space truncation remains accurate over time.

The approach is applicable to large systems with minimal error.

Abstract

By instantaneously changing a global parameter in an extended quantum system, an initially equilibrated state will afterwards undergo a complex non-equilibrium unitary evolution whose description is extremely challenging. A non-perturbative method giving a controlled error in the long time limit remained highly desirable to understand general features of the quench induced quantum dynamics. In this paper we show how integrability (via the algebraic Bethe ansatz) gives one numerical access, in a nearly exact manner, to the dynamics resulting from a global interaction quench of an ensemble of fermions with pairing interactions (Richardson's model). This possibility is deeply linked to the specific structure of this particular integrable model which gives simple expressions for the scalar product of eigenstates of two different Hamiltonians. We show how, despite the fact that a sudden quench can create excitations at any frequency, a drastic truncation of the Hilbert space can be carried out therefore allowing access to large systems. The small truncation error which results does not change with time and consequently the method grants access to a controlled description of the long time behavior which is a hard to reach limit with other numerical approaches.