Columnar Phase in Quantum Dimer Models

TL;DR

This paper proves that quantum dimer models exhibit long-range crystalline order at low temperatures with certain parameters, using reflection positivity, and extends the results to higher dimensions.

Contribution

It provides a rigorous proof of long-range order in quantum dimer models and generalizes the method to three-dimensional cases.

Findings

Long-range order established in quantum dimer models.

Reflection positivity as a key proof technique.

Results extendable to 3D models.

Abstract

The quantum dimer model, relevant for short-range resonant valence bond physics, is rigorously shown to have long range order in a crystalline phase in the attractive case at low temperature and not too large flipping term. This term flips horizontal dimer pairs to vertical pairs (and vice versa) and is responsible for the word `quantum' in the title. In addition to the dimers, monomers are also allowed. The mathematical method used is `reflection positivity'. The model and proof can easily be generalized to dimers or plaquettes in 3-dimensions.