Systematic strong coupling expansion for out-of-equilibrium dynamics in the Lieb-Liniger model

TL;DR

This paper develops a systematic strong coupling expansion to analyze the out-of-equilibrium dynamics of the Lieb-Liniger model after an interaction quench, providing detailed time-dependent local observable calculations.

Contribution

It introduces a $1/c$ expansion method for the Lieb-Liniger model's out-of-equilibrium dynamics, confirming the Quench Action approach's assumptions.

Findings

Derived leading terms of the $1/c$ expansion for local observables

Confirmed independence of results from the choice of representative state

Validated the typicality assumptions of the Quench Action approach

Abstract

We consider the time evolution of local observables after an interaction quench in the repulsive Lieb-Liniger model. The system is initialized in the ground state for vanishing interaction and then time-evolved with the Lieb-Liniger Hamiltonian for large, finite interacting strength $c$. We employ the Quench Action approach to express the full time evolution of local observables in terms of sums over energy eigenstates and then derive the leading terms of a $1/c$ expansion for several one and two-point functions as a function of time $t > 0$ after the quantum quench. We observe delicate cancellations of contributions to the spectral sums that depend on the details of the choice of representative state in the Quench Action approach and our final results are independent of this choice. Our results provide a highly non-trivial confirmation of the typicality assumptions underlying the Quench Action approach.