Overlap singularity and time evolution in integrable quantum field theory

TL;DR

This paper investigates the universal singularity at the two-particle threshold in integrable quantum field theory quenches, analyzes its implications for time evolution of observables, and explores potential experimental relevance.

Contribution

It demonstrates the inevitability of a two-particle singularity in homogeneous quenches with zero-momentum particles and constructs the time evolution of one-point functions including novel secular terms.

Findings

Identified a universal two-particle singularity at the threshold.

Derived a modified time dependence with a $t\ln t$ correction.

Discovered a new secular contribution related to parametric resonance.

Abstract

We study homogeneous quenches in integrable quantum field theory where the initial state contains zero-momentum particles. We demonstrate that the two-particle pair amplitude necessarily has a singularity at the two-particle threshold. Albeit the explicit discussion is carried out for special (integrable) initial states, we argue that the singularity is inevitably present and is a generic feature of homogeneous quenches involving the creation of zero momentum particles. We also identify the singularity in quenches in the Ising model across the quantum critical point, and compute it perturbatively in phase quenches in the quantum sine-Gordon model which are potentially relevant to experiments. We then construct the explicit time dependence of one-point functions using a linked cluster expansion regulated by a finite volume parameter. We find that the secular contribution normally linear in time is modified by a $t\ln t$ term. We additionally encounter a novel type of secular contribution which is shown to be related to parametric resonance. It is an interesting open question to resum the new contributions and to establish their consequences directly observable in experiments or numerical simulations.