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

TL;DR

This study uses variational Monte Carlo to analyze the entanglement entropy of a composite Fermi liquid state on a lattice, confirming the Widom formula's applicability and clarifying the role of wavefunction sign structure in entanglement scaling.

Contribution

It demonstrates that the Widom formula applies to the non-Fermi liquid composite Fermi liquid state, providing a quantitative link between wavefunction sign structure and entanglement entropy scaling.

Findings

The leading $L \, \log L$ term's prefactor matches that of free fermions.

The Widom formula holds for the CFL state despite its non-Fermi liquid nature.

Wavefunction sign structure influences entanglement scaling in gapless phases.

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.