Perturbative post-quench overlaps in quantum field theory

Kristóf Hódsági,Márton Kormos,Gábor Takács

doi:10.1007/jhep08(2019)047

Abstract

In analytic descriptions of quantum quenches, the overlaps between the initial pre-quench state and the eigenstates of the time evolving Hamiltonian are crucial ingredients. We construct perturbative expansions of these overlaps in quantum field theories where either the pre-quench or the post-quench Hamiltonian is integrable. Using the E8 Ising field theory for concrete computations, we give explicit expressions for the overlaps up to second order in the quench size, and verify our results against numerical results obtained using the Truncated Conformal Space Approach. We demonstrate that the expansion using the post-quench basis is very effective, but find some serious limitations for the alternative approach using the pre-quench basis.

Highlights

The current interest in the dynamics of quantum many-body systems out of equilibrium drives intensive research, both on the experimental and the theoretical side
It was discovered by studying quenches in the XXZ spin chain that the identification of the set of conserved charges necessary to build Generalised Gibbs Ensemble (GGE) is a non-trivial task [21,22,23,24] requiring the construction of new ‘quasi-local’ conserved quantities [25,26,27,28], with similar issues found in quantum field theories [29]
The first approach we developed is based on a perturbative expansion of the initial state in the basis of post-quench eigenstates. This approach is effective when the post-quench dynamics is integrable, since the required matrix elements can be expressed in terms of form factors which can often be constructed exactly using the form factor bootstrap

Summary

Introduction

The current interest in the dynamics of quantum many-body systems out of equilibrium drives intensive research, both on the experimental and the theoretical side. Thermalisation is absent for integrable systems and they are expected to reach a steady state described by a Generalised Gibbs Ensemble (GGE) [20] It was discovered by studying quenches in the XXZ spin chain that the identification of the set of conserved charges necessary to build GGE is a non-trivial task [21,22,23,24] requiring the construction of new ‘quasi-local’ conserved quantities [25,26,27,28], with similar issues found in quantum field theories [29]

Objectives

Methods

Conclusion