Quantum Kasteleyn transition

TL;DR

This paper introduces a quantum version of the Kasteleyn dimer model, revealing a phase transition from a dimer solid to a U(1) liquid, with exact critical coupling and detailed phase structure analysis.

Contribution

It presents the first quantum Kasteleyn model, analyzes its phase transition using string quantum mechanics, and calculates correlation functions near criticality.

Findings

Identified the exact critical coupling for the phase transition.

Described the phase structure at zero and nonzero temperature.

Calculated dimer-dimer correlation functions near the transition.

Abstract

Dimer models arise as effective descriptions in a variety of physical contexts, and provide paradigmatic examples of systems subject to strong local constraints. Here we present a quantum version of the venerable Kasteleyn model, which has an unusual phase transition from a dimer solid to a U(1) liquid. We show how the phase structure of the quantum model can be understood in terms of the quantum mechanics of one-dimensional strings and determine the exact value of the critical coupling. By constructing effective models to describe the properties of these strings, we calculate properties such as the dimer-dimer correlation function in the neighborhood of the transition. We also discuss the full phase structure of the model, in the ground state and at nonzero temperature.