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 $\lambda = 1$. 
D. Banerjee, M. B\"ogli, C. P. Hofmann, F.-J. Jiang, P. Widmer, and   U.-J. Wiese
cond-mat.str-el cond-mat.stat-mech hep-lat