Quantum quench in the Luttinger model with finite temperature initial state

TL;DR

This paper investigates the non-equilibrium dynamics of the Luttinger model after a quantum quench from a finite temperature initial state, revealing thermal features at high temperatures and analyzing energy statistics and fidelity decay.

Contribution

It provides a detailed analysis of how finite temperature initial states influence the dynamics and energy distributions in the Luttinger model after a quantum quench, including universal decay behavior.

Findings

High temperature initial states show thermal features in the steady state.

Uhlmann fidelity decays exponentially with temperature in the long time limit.

Energy and work distributions are affected by temperature, especially in small systems.

Abstract

We study the non-equilibrium dynamics of the Luttinger model after a quantum quench, when the initial state is a finite temperature thermal equilibrium state. The diagonal elements of the density matrix in the steady state show thermal features for high temperature initial states only, otherwise retain highly non-thermal character. The time evolution of Uhlmann fidelity, which measures the distance between the time evolved and initial states, is evaluated for arbitrary initial temperatures and quench protocols. In the long time limit, the overlap between the time evolved and initial system decreases exponentially with the temperature with a universal prefactor. Within perturbation theory, the statistics of final total energy and work are numerically evaluated in the case of a sudden quench, which yield identical distributions at zero temperature. In both statistics, temperature effects are more significant in small systems. The Dirac-delta peak at the adiabatic ground state energy remains present in the probability distribution of the total energy, but disappears from the work distribution at non-zero initial temperatures.