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

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 \(\lambda = 1\).