Disorder-Order Interface Propagating over the Ferromagnetic Ground State in the Transverse Field Ising Chain

TL;DR

This paper studies the dynamics of order parameters and entanglement at the interface between ordered and disordered regions in a transverse-field Ising chain, revealing universal scaling behaviors and entanglement properties.

Contribution

It provides analytical and numerical analysis of the universal scaling functions of correlations and entanglement asymmetries at the disorder-order interface in the transverse-field Ising chain.

Findings

Correlations follow universal asymptotic scaling functions.

Non-equal time correlations are also universal.

Wigner-Yanase skew information scales quadratically with subsystem length.

Abstract

We consider time evolution of order parameters and entanglement asymmetries in the ferromagnetic phase of the transverse-field Ising chain. One side of the system is prepared in a ferromagnetic ground state and the other side either in equilibrium at higher temperature or out of equilibrium. We focus on the disorder-order interface in which the order parameter attains a nonzero value, different from the ground state one. In that region, correlations follow a universal behaviour. We analytically compute the asymptotic scaling functions of the one- and two-point equal time correlations of the order parameter and provide numerical evidence that also the non-equal time correlations are universal. We analyze the R\'enyi entanglement asymmetries of subsystems and obtain a prediction that is expected to hold also in the von Neumann limit. Finally, we show that the Wigner-Yanase skew information of the order paramerter in subsystems within the interfacial region scales as their length squared. We propose a semiclassical approximation that is particularly effective close to the edge of the lightcone.