Full Counting Statistics in the Transverse Field Ising Chain

TL;DR

This paper derives a determinant formula for the full counting statistics of transverse magnetization in the Ising chain, analyzing its behavior in various states and after quantum quenches, revealing a multiple light-cone structure.

Contribution

It provides a novel determinant representation of the characteristic function for Gaussian states and analyzes its dynamics after quantum quenches.

Findings

Analytical expression for time and size dependence of the characteristic function.

Identification of a multiple light-cone structure in the dynamics.

Application to ground, thermal, and non-equilibrium steady states.

Abstract

We consider the full probability distribution for the transverse magnetization of a finite subsystem in the transverse field Ising chain. We derive a determinant representation of the corresponding characteristic function for general Gaussian states. We consider applications to the full counting statistics in the ground state, finite temperature equilibrium states, non-equilibrium steady states and time evolution after global quantum quenches. We derive an analytical expression for the time and subsystem size dependence of the characteristic function at sufficiently late times after a quantum quench. This expression features an interesting multiple light-cone structure.