Entanglement entropy of critical spin liquids

TL;DR

This paper calculates the bipartite entanglement entropy of critical spin liquids, revealing a violation of the boundary law due to emergent fermions, using variational Monte Carlo on large systems.

Contribution

It introduces a method to compute the Renyi entropy of non-sign positive wavefunctions, demonstrating boundary law violation in a critical spin liquid.

Findings

Entanglement entropy violates the boundary law with a logarithmic enhancement.

The method applies to large systems (>324 spins).

Emergent fermions influence the entanglement properties.

Abstract

Quantum spin liquids are phases of matter whose internal structure is not captured by a local order parameter. Particularly intriguing are critical spin liquids, where strongly interacting excitations control low energy properties. Here we calculate their bipartite entanglement entropy that characterize their quantum structure. In particular we calculate the Renyi entropy $S_2$, on model wavefunctions obtained by Gutzwiller projection of a Fermi sea. Although the wavefunctions are not sign positive, $S_2$ can be calculated on relatively large systems (>324 spins), using the variational Monte Carlo technique. On the triangular lattice we find that entanglement entropy of the projected Fermi-sea state violates the boundary law, with $S_2$ enhanced by a logarithmic factor. This is an unusual result for a bosonic wave-function reflecting the presence of emergent fermions. These techniques can be extended to study a wide class of other phases.