Entanglement studies of resonating valence bonds on the frustrated square lattice

TL;DR

This paper investigates the entanglement properties of a specific resonating valence bond wave function on a frustrated square lattice, revealing its topological nature and providing new insights into quantum dimer models and lattice topologies.

Contribution

It introduces a method to identify minimum entropy states in RVB wave functions and links them to quantum dimer models, confirming the $ ext{Z}_2$ topological order.

Findings

The topological entanglement entropy is approximately ln(2).

MES states relate to eigenstates of a 't Hooft operator.

The concept of a 'pre-Kasteleyn' orientation is proposed.

Abstract

We study a short-range resonating valence bond (RVB) wave function with diagonal links on the square lattice that permits sign-problem free wave function Monte-Carlo studies. Special attention is given to entanglement properties, in particular, the study of minimum entropy states (MES) according to the method of Zhang et. al. [Physical Review B {\bf 85}, 235151 (2012)]. We provide evidence that the MES associated with the RVB wave functions can be lifted from an associated quantum dimer picture of these wave functions, where MES states are certain linear combinations of eigenstates of a 't Hooft "magnetic loop"-type operator. From this identification, we calculate a value consistent with $\ln(2)$ for the topological entanglement entropy directly for the RVB states via wave function Monte-Carlo. This corroborates the $\mathbb{Z}_{2}$ nature of the RVB states. We furthermore define and elaborate on the concept of a "pre-Kasteleyn" orientation that may be useful for the study of lattices with non-planar topology in general.