Non-equilibrium quantum dynamics after local quenches

TL;DR

This paper investigates the non-equilibrium quantum dynamics of a one-dimensional transverse Ising chain after a local quench, analyzing magnetization and correlation functions across different phases and comparing with theoretical predictions.

Contribution

It provides a detailed analysis of the time evolution of magnetization and correlations after a local quench in the transverse Ising model, including finite size scaling and comparison with conformal field theory.

Findings

Finite size scaling forms at the critical point.

Agreement with conformal field theory predictions.

Magnetization profiles match quasi-classical calculations in the ferromagnetic phase.

Abstract

We study the quantum dynamics resulting from preparing a one-dimensional quantum system in the ground state of initially two decoupled parts which are then joined together (local quench). Specifically we focus on the transverse Ising chain and compute the time-dependence of the magnetization profile, m_l(t), and correlation functions at the critical point, in the ferromagnetically ordered phase and in the paramagnetic phase. At the critical point we find finite size scaling forms for the nonequilibrium magnetization and compare predictions of conformal field theory with our numerical results. In the ferromagnetic phase the magnetization profiles are well matched by our predictions from a quasi-classical calculation.