• DOI:10.1103/PhysRevB.100.035124
• Corpus ID: 119187223

Functional field integral approach to quantum work

@article{Dong2019FunctionalFI,
  title={Functional field integral approach to quantum work},
  author={Jian-Jun Dong and Yi-feng Yang},
  journal={Physical Review B},
  year={2019}
}

• Jian-Jun Dong, Yi-feng Yang
• Published 3 January 2019
• Physics
• Physical Review B

We introduce the functional field integral approach to study the statistics of quantum work for arbitrary nonequilibrium process. For a general bilinear Hamiltonian with a sudden quench of the control parameters, we derive the analytical formalism for the characteristic function, the mean work density and mean irreversible work density. We show that the mean irreversible work may be used to detect quantum phase transitions and exhibit characteristic scaling at the quantum critical point for a single quench process. For a double quench process, a dynamical quantum phase transition may occur as a singularity in the so-called rate function. We examine our method in three models: the transverse Ising chain, the Su-Schrieffer-Heeger (SSH) model and the Bardeen-Cooper-Schrieffer (BCS) Hamiltonian for superconductivity. Our results for the Ising chain is in agreement with the Hamiltonian approach and yield the correct scaling exponents, while for the SSH model, we find nonuniversal quantum critical scaling due to the topological nature of its quantum phase transition. Quantum critical scaling and dynamical quantum phase transition were also obtained in the BCS model with single or double quench protocols in combination with the mean-field approximation. This suggests that our approach may be potentially extended to other many-body systems for future investigation of their dynamical properties under nonequilibrium condition.