Interacting classical dimers on the square lattice

TL;DR

This paper investigates a classical dimer model on the square lattice with interactions, revealing a Kosterlitz-Thouless transition between ordered and critical phases, with implications for quantum dimer models.

Contribution

It introduces a detailed analysis of the classical limit of quantum dimer models, identifying phase transitions and constructing the Coulomb gas representation.

Findings

Identifies a Kosterlitz-Thouless transition in the model.

Characterizes the low temperature ordered phase and high temperature critical phase.

Computes the Coulomb gas coupling constant numerically.

Abstract

We study a model of close-packed dimers on the square lattice with a nearest neighbor interaction between parallel dimers. This model corresponds to the classical limit of quantum dimer models [D.S. Rokhsar and S.A. Kivelson, Phys. Rev. Lett.{\bf 61}, 2376 (1988)]. By means of Monte Carlo and Transfer Matrix calculations, we show that this system undergoes a Kosterlitz-Thouless transition separating a low temperature ordered phase where dimers are aligned in columns from a high temperature critical phase with continuously varying exponents. This is understood by constructing the corresponding Coulomb gas, whose coupling constant is computed numerically. We also discuss doped models and implications on the finite-temperature phase diagram of quantum dimer models.