Breakdown of quantum-classical correspondence and dynamical generation of entanglement

TL;DR

This paper analytically investigates how the exchange interaction in an isolated Fermi gas causes the breakdown of quantum-classical correspondence, leading to entanglement growth and thermalization within the system, supporting a key conjecture on quantum thermalization.

Contribution

It provides an analytical solution demonstrating the dynamical generation of entanglement and thermalization in a chaotic Fermi gas, confirming a conjecture on quantum thermalization.

Findings

Breakdown of quantum-classical correspondence affects entanglement structure.

Subsystems reach thermal equilibrium with entropy equal to entanglement entropy.

Analytical support for a conjecture on quantum thermalization by Garrison and Grover.

Abstract

The {\it exchange} interaction arising from the particle indistinguishability is of central importance to physics of many-particle quantum systems. Here we study analytically the dynamical generation of quantum entanglement induced by this interaction in an isolated system, namely, an ideal Fermi gas confined in a chaotic cavity, which evolves unitarily from a non-Gaussian pure state. We find that the breakdown of the quantum-classical correspondence of particle motion, via dramatically changing the spatial structure of many-body wavefunction, leads to profound changes of the entanglement structure. Furthermore, for a class of initial states, such change leads to the approach to thermal equilibrium everywhere in the cavity, with the well-known Ehrenfest time in quantum chaos as the thermalization time. Specifically, the quantum expectation values of various correlation functions at different spatial scales are all determined by the Fermi-Dirac distribution. In addition, by using the reduced density matrix (RDM) and the entanglement entropy (EE) as local probes, we find that the gas inside a subsystem is at equilibrium with that outside, and its thermal entropy is the EE, even though the whole system is in a pure state. As a by-product of this work, we provide an analytical solution supporting an important conjecture on thermalization, made and numerically studied by Garrison and Grover in: Phys. Rev. X \textbf{8}, 021026 (2018), and strengthen its statement.