Interfaces, Strings, and a Soft Mode in the Square Lattice Quantum Dimer Model

TL;DR

This study investigates the square lattice quantum dimer model, revealing a confining phase with fractionalized flux tubes and a soft mode, using quantum Monte Carlo simulations to explore its phases and excitations.

Contribution

It provides new insights into the phase structure and excitations of the square lattice quantum dimer model, including the emergence of a soft mode and fractionalized flux tubes.

Findings

Confined columnar phase for λ<1

Interfaces exhibit plaquette order without bulk realization

Presence of a soft pseudo-Goldstone mode around λ≈0

Abstract

The quantum dimer model on the square lattice is equivalent to a $U(1)$ gauge theory. Quantum Monte Carlo calculations reveal that, for values of the Rokhsar-Kivelson (RK) coupling $\lambda < 1$, the theory exists in a confining columnar phase. The interfaces separating distinct columnar phases display plaquette order, which, however, is not realized as a bulk phase. Static "electric" charges are confined by flux tubes that consist of multiple strands, each carrying a fractionalized flux $\frac{1}{4}$. A soft pseudo-Goldstone mode emerges around $\lambda \approx 0$, long before one reaches the RK point at $\lambda = 1$.