Quench Dynamics of the Gaudin-Yang Model

TL;DR

This paper investigates the quench dynamics of the Gaudin-Yang model, a quantum integrable system describing 1D bosonic or fermionic gases, using the Yudson approach to analyze eigenstates and correlations.

Contribution

It introduces a contour integral method to expand initial states in terms of Bethe Ansatz eigenstates, including bound states beyond the standard String hypothesis.

Findings

Complete set of eigenstates including bound states obtained

Density and noise correlations calculated for quenched systems

Demonstrates the larger Hilbert space structure of the model

Abstract

We study the quench dynamics of one dimensional bosons or fermion quantum gases with either attractive or repulsive contact interactions. Such systems are well described by the Gaudin-Yang model which turns out to be quantum integrable. We use a contour integral approach, the Yudson approach, to expand initial states in terms of Bethe Ansatz eigenstates of the Hamiltonian. Making use of the contour, we obtain a complete set of eigenstates, including both free states and bound states. These states constitute a larger Hilbert space than described by the standard String hypothesis. We calculate the density and noise correlations of several quenched systems such as a static or kinetic impurity evolving in an array of particles.