Dynamics in the Ising field theory after a quantum quench

TL;DR

This paper develops a new analytical method to study the real-time evolution of the order parameter in the Ising field theory after a quantum quench, extending previous lattice results to the continuum limit.

Contribution

It introduces a formalism for handling divergences in field theory quenches, generalizing existing lattice-based approaches to continuum integrable models.

Findings

Successfully resummed divergent terms in the form-factor expansion.

Reproduced known lattice results in the scaling limit.

Provided a generalizable method for other integrable models.

Abstract

We study the real-time dynamics of the order parameter $<\sigma(t)>$ in the Ising field theory after a quench in the fermion mass, which corresponds to a quench in the transverse field of the corresponding transverse field Ising chain. We focus on quenches within the ordered phase. The long-time behaviour is obtained analytically by a resummation of the leading divergent terms in a form-factor expansion for $<\sigma(t)>$. Our main result is the development of a method for treating divergences associated with working directly in the field theory limit. We recover the scaling limit of the corresponding result by Calabrese et al. [Phys. Rev. Lett. \textbf{106}, 227203 (2011)], which was obtained for the lattice model. Our formalism generalizes to integrable quantum quenches in other integrable models.