Functional field integral approach to quantum work

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.

13 pages, 9 figures

References in corpus (13)

• Many-Body Physics with Ultracold Gases
• Fluctuation theorems: Work is not an observable
• Experimental Test of Quantum Jarzynski Equality with a Trapped Ion System
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Large deviations and universality in quantum quenches
• Assessing the non-equilibrium thermodynamics in a quenched quantum many-body system via single projective measurements
• Jarzynski equation for a simple quantum system: Comparing two definitions of work
• Generalized Gibbs ensemble and work statistics of a quenched Luttinger liquid
• Work distribution and path integrals in general mean-field systems
• Characterization of topological phases of modified dimerized Kitaev chain via edge correlation functions
• Exact solution to an interacting dimerized Kitaev model at symmetric point
• Quench echo and work statistics in integrable quantum field theories
• Understanding quantum work in a quantum many-body system