# Ballistic front dynamics after joining two semi-infinite quantum Ising chains

## TL;DR

This paper studies the non-equilibrium energy transport and front dynamics in joined quantum Ising chains, revealing universal scaling behaviors and novel edge phenomena depending on the criticality of the transverse field.

## Contribution

It extends previous models by providing a full space-time description of energy and quasi-particle densities after joining two quantum Ising chains, including new universal edge scaling forms.

## Key findings

- Different behaviors at the propagating front depending on criticality
- Emergence of a new universal scaling form at the edge
- Corrections to leading behavior described by Airy kernel in non-critical case

## Abstract

We consider two semi-infinite quantum Ising chains initially at thermal equilibrium at two different temperatures and subsequently joined by an interaction between their end points. Transport properties such as the heat current are determined by the dynamics of the left- and right-moving fermionic quasi-particles which characterize the ensuing unitary dynamics. Within the so-called semi-classical space-time scaling limit we extend known results by determining the full space and time dependence of the density and current of energy and of fermionic quasi-particles. Upon approaching the edge of the propagating front, these quantities as well as the two-point correlation function display qualitatively different behaviors depending on the transverse field of the chain being critical or not. While in the latter case corrections to the leading behavior are described, as expected, by the Airy kernel, in the former a novel scaling form emerges with universal features.