# Functional field integral approach to quantum work

## TL;DR

This paper develops a functional field integral method to analyze quantum work statistics in nonequilibrium quantum systems, successfully applying it to models like the transverse Ising chain, SSH model, and BCS superconductivity.

## Contribution

It introduces a novel, numerically simple formalism for quantum work analysis applicable to various models, including topological and superconducting systems.

## Key findings

- Correct quantum critical scaling in the transverse Ising chain.
- Observation of nonuniversal scaling in the SSH model.
- Detection of dynamical quantum phase transitions in multiple protocols.

## Abstract

We introduce the functional field integral approach to study the statistics of quantum work under nonequilibrium conditions and derive the general formalism for a bilinear Hamiltonian with arbitrary time dependence. The method is then examined in three models. For the transverse Ising chain, it yields the correct quantum critical scaling and dynamical quantum phase transitions for single and double quench protocols, respectively. For the Su-Schrieffer-Heeger (SSH) model, we observe nonuniversal quantum critical scaling with anomalous $1/N$-correction due to its topological nature. Dynamical quantum phase transitions are observed for three different time evolution protocols but their time periodicity only appears in the double quench case. We then extend our method to the Bardeen-Cooper-Schrieffer (BCS) model for superconductivity and discuss the possibility of its application for general correlated models in combination with either the mean-field approximation or exact Monte Carlo simulations on classical (auxiliary) fields or disorders. Our method has the advantage of numerical simplicity, in the cost of explicit state evolution, and provides a promising way for exploring the physics of quantum work under general conditions.