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∼L^(d−1) log L . Using variational Monte Carlo, we calculate the second Rényi entropy for a model wave function of the ν=1/2 composite Fermi liquid (CFL) state defined on the two-dimensional triangular lattice. By carefully studying the scaling of the total Rényi entropy and, crucially, its contributions from the modulus and sign of the wave function 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 wave function. In contrast to the recent results of Shao et al. [Phys. Rev. Lett. 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 wave function sign structure and S∼L log L entanglement scaling in such highly entangled gapless phases.

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