Finite-temperature entanglement negativity of free fermions

TL;DR

This paper investigates how finite temperature influences the entanglement negativity in free fermion systems, revealing a crossover from quantum entanglement to classical thermal states and providing analytical and numerical insights across dimensions.

Contribution

The paper derives the finite-temperature entanglement negativity for free fermions and generalizes the results to higher dimensions with arbitrary Fermi surface shapes.

Findings

Entanglement negativity decreases with temperature, indicating loss of quantum entanglement.

Analytical results match numerical simulations in one and two dimensions.

Crossover from quantum to classical states is characterized by negativity behavior.

Abstract

The entanglement entropy of free fermions with a Fermi surface is known to obey a logarithmic scaling and violate the area law in all dimensions. Here, we would like to see how temperature affects the logarithmic scaling behavior. To this end, we compute the entanglement negativity of free fermions using the fermionic partial transpose developed in our earlier paper [Phys. Rev. B 95, 165101 (2017)]. In one dimension, we analytically derive the leading order term in the finite-temperature entanglement negativity and show how the entanglement negativity indicates a crossover from a quantum entangled state to a classical thermal state, where the entanglement is completely lost. We explain how the one-dimensional result can be generalized to codimension-one Fermi surface of arbitrary shape in higher dimensions. In both one and two dimensions, we check that our analytical results agree with the numerical simulation of free fermions on a lattice.