Entanglement measures and non-equilibrium dynamics of quantum many-body systems: a path integral approach

TL;DR

This paper develops a path integral formalism to compute entanglement measures and analyze non-equilibrium dynamics in quantum many-body systems, offering a new approach that simplifies calculations and extends to driven out-of-equilibrium scenarios.

Contribution

It introduces a novel path integral method to evaluate entanglement and dynamics in Gaussian quantum many-body systems, avoiding Keldysh techniques and applicable to driven out-of-equilibrium models.

Findings

Expressed entanglement measures in terms of Matsubara Green functions.

Applied formalism to the 2D Bose-Hubbard model with gauge fields.

Derived analytical expressions for return probability and counting statistics.

Abstract

We present a path integral formalism for expressing matrix elements of the density matrix of a quantum many-body system between any two coherent states in terms of standard Matsubara action with periodic(anti-periodic) boundary conditions on bosonic(fermionic) fields. We show that this enables us to express several entanglement measures for bosonic/fermionic many-body systems described by a Gaussian action in terms of the Matsubara Green function. We apply this formalism to compute various entanglement measures for the two-dimensional Bose-Hubbard model in the strong-coupling regime, both in the presence and absence of Abelian and non-Abelian synthetic gauge fields, within a strong coupling mean-field theory. In addition, our method provides an alternative formalism for addressing time evolution of quantum-many body systems, with Gaussian actions, driven out of equilibrium without the use of Keldysh technique. We demonstrate this by deriving analytical expressions of the return probability and the counting statistics of several operators for a class of integrable models represented by free Dirac fermions subjected to a periodic drive in terms of the elements of their Floquet Hamiltonians. We provide a detailed comparison of our method with the earlier, related, techniques used for similar computations, discuss the significance of our results, and chart out other systems where our formalism can be used.