Entanglement in gapless resonating valence bond states

TL;DR

This paper investigates the entanglement properties of gapless resonating valence bond states on the square lattice, revealing similarities between spin and dimer RVB states and highlighting the sensitivity of entanglement entropy to the Re9nyi index.

Contribution

It provides exact calculations and numerical evidence showing the entanglement entropy behavior in RVB states and introduces an effective theory interpolating between different RVB states.

Findings

Entanglement entropy exhibits a logarithmic behavior similar to 1D systems.

Large Re9nyi index reveals an even/odd effect in entanglement entropy.

Numerical results support the effective theory interpolating between RVB states.

Abstract

We study resonating-valence-bond (RVB) states on the square lattice of spins and of dimers, as well as SU(N)-invariant states that interpolate between the two. These states are ground states of gapless models, although the SU(2)-invariant spin RVB state is also believed to be a gapped liquid in its spinful sector. We show that the gapless behavior in spin and dimer RVB states is qualitatively similar by studying the R\'enyi entropy for splitting a torus into two cylinders, We compute this exactly for dimers, showing it behaves similarly to the familiar one-dimensional log term, although not identically. We extend the exact computation to an effective theory believed to interpolate among these states. By numerical calculations for the SU(2) RVB state and its SU(N)-invariant generalizations, we provide further support for this belief. We also show how the entanglement entropy behaves qualitatively differently for different values of the R\'enyi index $n$, with large values of $n$ proving a more sensitive probe here, by virtue of exhibiting a striking even/odd effect.