Interfaces, strings, and a soft mode in the square lattice quantum dimer model

Abstract

The quantum dimer model on the square lattice is a $\text{U}(1)$ gauge theory that addresses aspects of the physics of high-${T}_{c}$ superconductors. Using a quantum Monte Carlo method, we show that the theory exists in a confining columnar valence bond solid 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 (which becomes exactly massless at the Rokhsar-Kivelson point) extends deep into the columnar phase, with potential implications for high-${T}_{c}$ physics.