On computing non-equilibrium dynamics following a quench

TL;DR

This paper introduces a numerical method to efficiently compute non-equilibrium dynamics after a quantum quench, overcoming the challenge of calculating state overlaps in exactly solvable models.

Contribution

It develops a non-perturbative numerical approach combining high overlap state generation and a modified renormalization group for Lieb-Liniger model dynamics.

Findings

Effective in computing post-quench dynamics in Lieb-Liniger model

Applicable to both continuum and lattice systems

Extensible to scenarios with broken integrability

Abstract

Computing the non-equilibrium dynamics that follows a quantum quench is difficult, even in exactly solvable models. Results are often predicated on the ability to compute overlaps between the initial state and eigenstates of the Hamiltonian that governs time evolution. Except for a handful of known cases, it is generically not possible to find these overlaps analytically. Here we develop a numerical approach to preferentially generate the states with high overlaps for a quantum quench starting from the ground state or an excited state of an initial Hamiltonian. We use these preferentially generated states, in combination with a "high overlap states truncation scheme" and a modification of the numerical renormalization group, to compute non-equilibrium dynamics following a quench in the Lieb-Liniger model. The method is non-perturbative, works for reasonable numbers of particles, and applies to both continuum and lattice systems. It can also be easily extended to more complicated scenarios, including those with integrability breaking.