Hole statistics and superfluid phases in quantum dimer models

Abstract

Quantum dimer models (QDMs) arise as low-energy effective models for frustrated magnets. Some of these models have proven successful in generating a scenario for exotic spin liquid phases with deconfined spinons. Doping, i.e., the introduction of mobile holes, has been considered within the QDM framework and partially studied. A fundamental issue is the possible existence of a superconducting phase in such systems and its properties. For this purpose, the question of the statistics of the mobile holes (or ``holons'') shall be addressed first. Such issues are studied in detail in this paper for generic doped QDMs defined on the most common two-dimensional lattices (square, triangular, honeycomb, kagome, \dots{}) and involving general resonant loops. We prove a general ``statistical transmutation'' symmetry of such doped QDMs by using composite operators of dimers and holes. This exact transformation enables us to define duality equivalence classes (or families) of doped QDMs, and provides the analytic framework to analyze dynamical statistical transmutations. We discuss various possible superconducting phases of the system. In particular, the possibility of an exotic superconducting phase originating from the condensation of (bosonic) charge-$e$ holons is examined. A numerical evidence of such a superconducting phase is presented in the case of the triangular lattice, by introducing a gauge-invariant holon Green's function. We also make the connection with a Bose-Hubbard model on the kagome lattice which gives rise, as an effective model in the limit of strong interactions, to a doped QDM on the triangular lattice.