Entanglement entropy of composite Fermi liquid states on the lattice: In support of the Widom formula

Abstract

Quantum phases characterized by surfaces of gapless excitations are known to violate the otherwise ubiquitous boundary law of entanglement entropy in the form of a multiplicative log correction: $S\sim L^{d-1} \log L$. Using variational Monte Carlo, we calculate the second R\'enyi entropy for a model wavefunction of the $\nu=1/2$ composite Fermi liquid (CFL) state defined on the two-dimensional triangular lattice. By carefully studying the scaling of the total R\'enyi entropy and, crucially, its contributions from the modulus and sign of the wavefunction on various finite-size geometries, we argue that the prefactor of the leading $L \log L$ term is equivalent to that in the analogous free fermion wavefunction. In contrast to the recent results of Shao et al. [PRL 114, 206402 (2015)], we thus conclude that the "Widom formula" holds even in this non-Fermi liquid CFL state. More generally, our results further elucidate---and place on a more quantitative footing---the relationship between nontrivial wavefunction sign structure and $S\sim L \log L$ entanglement scaling in such highly entangled gapless phases.