Engineering SU(2) invariant spin models to mimic quantum dimer physics on the square lattice

TL;DR

This paper constructs and analyzes SU(2) invariant spin models that mimic quantum dimer physics, revealing an unusual spin liquid phase with gapless excitations and phase transitions to ordered states.

Contribution

It extends previous models to a continuous family of SU(2) invariant spin models that replicate the quantum dimer phase diagram, including columnar and staggered phases.

Findings

Support for gapless spinless excitations

Existence of a spin gap in the thermodynamic limit

Evidence for phase transitions to ordered phases

Abstract

We consider the spin-1/2 hamiltonians proposed by Cano and Fendley [J. Cano and P. Fendley, Phys. Rev. Lett. 105, 067205 (2010)] which were built to promote the well-known Rokshar-Kivelson (RK) point of quantum dimer models to spin-1/2 wavefunctions. We first show that these models, besides the exact degeneracy of RK point, support gapless spinless excitations as well as a spin gap in the thermodynamic limit, signatures of an unusual spin liquid. We then extend the original construction to create a continuous family of SU(2) invariant spin models that reproduces the phase diagram of the quantum dimer model, and in particular show explicit evidences for existence of columnar and staggered phases. The original models thus appear as multicritical points in an extended phase diagram. Our results are based on the use of a combination of numerical exact simulations and analytical mapping to effective generalized quantum dimer models.