Entanglement signatures of quantum-to-classical crossover of a Fermi surface

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 thermal fluctuations affect the logarithmic scaling behavior. To this end, we analytically compute the bipartite entanglement negativity of a finite-temperature state and show that the coherent Fermi surface is gradually destroyed as a function of temperature and eventually turns into an incoherent classical system, where the entanglement is completely lost. We check that our analytical results agree with the numerical simulation of free fermions on a lattice.