Statistics of holes and nature of superfluid phases in Quantum dimer models

TL;DR

This paper investigates the statistical properties and potential superconducting phases of doped quantum dimer models on various 2D lattices, revealing a symmetry that relates different statistics and providing evidence for exotic superconductivity.

Contribution

It introduces a general statistical transmutation symmetry in doped QDMs and explores the emergence of exotic superconducting phases, supported by numerical evidence on the triangular lattice.

Findings

Proves a statistical transmutation symmetry in doped QDMs.

Identifies duality classes of doped QDMs based on this symmetry.

Provides numerical evidence for a bosonic charge-e holon condensate on the triangular lattice.

Abstract

Quantum Dimer Models (QDM) 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 details in this paper for generic doped QDM defined on the most common two-dimensional lattices (square, triangular, honeycomb, kagome,...) and involving general resonant loops. We prove a general "statistical transmutation" symmetry of such doped QDM by using composite operators of dimers and holes. This exact transformation enables to define duality equivalence classes (or families) of doped QDM, 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 novel 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.