Finite temperature fidelity susceptibility for one-dimensional quantum systems

TL;DR

This paper investigates the temperature dependence of fidelity susceptibility in one-dimensional quantum systems, introduces a lattice path integral algorithm for its calculation, and validates findings with models including free fermions and the XXZ chain.

Contribution

It develops a universal linear-in-temperature correction to fidelity susceptibility and introduces a novel lattice path integral method for thermodynamic limit calculations.

Findings

Universal linear temperature contribution to fidelity susceptibility.

Algorithm successfully computes F(T) in the thermodynamic limit.

Validation with free fermions and XXZ chain confirms theoretical predictions.

Abstract

We calculate the fidelity susceptibility chi_f for the Luttinger model and show that there is a universal contribution linear in temperature T (or inverse length 1/L). Furthermore, we develop an algorithm - based on a lattice path integral approach - to calculate the fidelity F(T) in the thermodynamic limit for one-dimensional quantum systems. We check the Luttinger model predictions by calculating chi_f(T) analytically for free spinless fermions and numerically for the XXZ chain. Finally, we study chi_f at the two phase transitions in this model.