# Perturbative post-quench overlaps in Quantum Field Theory

## TL;DR

This paper develops perturbative methods to compute overlaps between initial and eigenstates in quantum quenches within quantum field theories, validated by explicit calculations in the E8 Ising model.

## Contribution

It introduces a perturbative expansion framework for overlaps in quantum quenches, especially when either Hamiltonian is integrable, with explicit second-order results and numerical validation.

## Key findings

- Post-quench basis expansion is highly effective.
- Pre-quench basis expansion has significant limitations.
- Explicit second-order overlap expressions for E8 Ising theory.

## 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 $E_8$ 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.