Coherent-state path integrals in quantum thermodynamics

TL;DR

This paper clarifies the use of coherent-state path integrals in quantum thermodynamics, demonstrating their equivalence to Hamiltonian methods across various many-particle systems with careful handling of subtleties.

Contribution

It provides a detailed analysis of subtle issues in coherent-state path integrals and shows their correct application to quantum thermodynamic systems, ensuring consistent results with traditional methods.

Findings

Path integrals yield results identical to Hamiltonian approaches when handled carefully.

Illustrated with paradigmatic systems including harmonic oscillators and Hubbard models.

Clarified subtleties in continuum evaluations in imaginary time and Matsubara space.

Abstract

In these notes, we elucidate some subtle aspects of coherent-state path integrals, focusing on their application to the equilibrium thermodynamics of quantum many-particle systems. These subtleties emerge when evaluating path integrals in the continuum, either in imaginary time or in Matsubara-frequency space. Our central message is that, when handled with due care, the path integral yields results identical to those obtained from the canonical Hamiltonian approach. We illustrate this through a pedagogical treatment of several paradigmatic systems: the bosonic and fermionic harmonic oscillators, the single-site Bose-Hubbard and Hubbard models, the weakly-interacting Bose gas with finite-range interactions, and the BCS superconductor with finite-range interactions.