Finite-Volume Energy Spectrum, Fractionalized Strings, and Low-Energy Effective Field Theory for the Quantum Dimer Model on the Square Lattice

TL;DR

This paper provides a comprehensive analytic and numerical study of the square lattice quantum dimer model, revealing fractionalization of strings, emergent symmetries, and a low-energy effective field theory that describes its confining phase.

Contribution

It introduces a systematic low-energy effective field theory for the quantum dimer model, explaining fractionalization and emergent symmetries, supported by exact diagonalization and Monte Carlo data.

Findings

String fractionalization into eight strands with electric flux 1/4

Existence of a pseudo-Goldstone boson with approximate SO(2) symmetry

Confirmation of the columnar phase up to the Rokhsar-Kivelson point

Abstract

We present detailed analytic calculations of finite-volume energy spectra, mean field theory, as well as a systematic low-energy effective field theory for the square lattice quantum dimer model. The analytic considerations explain why a string connecting two external static charges in the confining columnar phase fractionalizes into eight distinct strands with electric flux $\frac{1}{4}$. An emergent approximate spontaneously broken $SO(2)$ symmetry gives rise to a pseudo-Goldstone boson. Remarkably, this soft phonon-like excitation, which is massless at the Rokhsar-Kivelson (RK) point, exists far beyond this point. The Goldstone physics is captured by a systematic low-energy effective field theory. We determine its low-energy parameters by matching the analytic effective field theory with exact diagonalization results and Monte Carlo data. This confirms that the model exists in the columnar (and not in a plaquette or mixed) phase all the way to the RK point.