Nodal Line Entanglement Entropy: Generalized Widom Formula from Entanglement Hamiltonians

Understand

A system of fermions forming a Fermi surface exhibits a large degree of quantum entanglement, even in the absence of interactions.

• In particular, the usual case of a codimension one Fermi surface leads to a logarithmic violation of the area law for entanglement entropy, as dictated by the Widom formula.
• We here generalize this formula to the case of arbitrary codimension, which is of particular interest for nodal lines in three dimensions.
• We first rederive the standard Widom formula by calculating an entanglement Hamiltonian for Fermi surface systems, obtained by repurposing a trick commonly applied to relativistic theories.