Quantum criticality, lines of fixed points, and phase separation in doped two-dimensional quantum dimer models

TL;DR

This paper explores the phase diagram of doped quantum dimer models on a square lattice, revealing a rich structure of critical, liquid, and phase-separated states influenced by doping and interactions.

Contribution

It introduces an analytic and Monte Carlo study of doped quantum dimer models, identifying lines of critical points, phase separation, and the effects of hole interactions.

Findings

Existence of a Kosterlitz-Thouless transition at zero doping.

Identification of a dimer-hole liquid phase at low doping.

Discovery of a multicritical point where the transition becomes first order.

Abstract

We study phase diagrams of a class of doped quantum dimer models on the square lattice with ground-state wave functions whose amplitudes have the form of the Gibbs weights of a classical doped dimer model. In this dimer model, parallel neighboring dimers have attractive interactions, whereas neighboring holes either do not interact or have a repulsive interaction. We investigate the behavior of this system via analytic methods and by Monte Carlo simulations. At zero doping, we confirm the existence of a Kosterlitz-Thouless transition from a quantum critical phase to a columnar phase. At low hole densities we find a dimer-hole liquid phase and a columnar phase, separated by a phase boundary which is a line of critical points with varying exponents. We demonstrate that this line ends at a multicritical point where the transition becomes first order and the system phase separates. The first-order transition coexistence curve is shown to become unstable with respect to more complex inhomogeneous phases in the presence of direct hole-hole interactions. We also use a variational approach to determine the spectrum of low-lying density fluctuations in the dimer-hole fluid phase.