On the theory of quantum quenches in near-critical systems

TL;DR

This paper extends the theory of quantum quenches in near-critical one-dimensional systems, analyzing relaxation dynamics, operator scaling, and spectral features, highlighting differences between non-interacting and interacting cases.

Contribution

It provides new insights into the relaxation values of one-point functions, relates these to operator scaling dimensions, and explores spectral accessibility through quenches.

Findings

Relaxation values relate to operator scaling dimensions.

Undamped oscillations occur only in interacting systems.

Spectral features like the $E_8$ spectrum are more accessible via quenches.

Abstract

The theory of quantum quenches in near-critical one-dimensional systems formulated in [J. Phys. A 47 (2014) 402001] yields analytic predictions for the dynamics, unveils a qualitative difference between non-interacting and interacting systems, with undamped oscillations of one-point functions occurring only in the latter case, and explains the presence and role of different time scales. Here we examine additional aspects, determining in particular the relaxation value of one-point functions for small quenches. For a class of quenches we relate this value to the scaling dimensions of the operators. We argue that the $E_8$ spectrum of the Ising chain can be more accessible through a quench than at equilibrium, while for a quench of the plane anisotropy in the XYZ chain we obtain that the one-point function of the quench operator switches from damped to undamped oscillations at $\Delta=1/2$.