Exact Spin Liquid Ground States of the Quantum Dimer Model on the Square and Honeycomb Lattices

TL;DR

This paper constructs exact ground states for a generalized quantum dimer model on square and honeycomb lattices, revealing short-range correlations and topological degeneracy indicative of a gapped spin liquid phase.

Contribution

It introduces exact ground states for a generalized quantum dimer model, linking them to Grassmann fields and identifying signatures of gapped spin liquids.

Findings

Ground states are exactly constructed at generalized RK points.

Ground-state correlations are short-ranged in the small second neighbor dimer limit.

Ground states show fourfold topological degeneracy on a torus.

Abstract

We study a generalized quantum hard-core dimer model on the square and honeycomb lattices, allowing for first and second neighbor dimers. At generalized RK points, the exact ground states can be constructed, and ground-state correlation functions can be equated to those of interacting 1+1 dimensional Grassmann fields. When the concentration of second neighbor dimers is small, the ground state correlations are shown to be short-ranged corresponding to a (gaped) spin liquid phase. On a 2-torus, the ground states exhibit fourfold topological degeneracy. On a finite cylinder we have found a dramatic even-odd effect depending on the circumference, and propose that this can be used as a numerical diagnostic of gapped spin-liquid phases, more generally.