Statistical transmutation in doped quantum dimer models

TL;DR

This paper proves a symmetry in doped quantum dimer models that allows for a duality between different statistical descriptions of holes, enabling analysis of phase behaviors in various lattice geometries.

Contribution

It introduces an exact statistical transmutation symmetry in doped quantum dimer models and explores its implications for phase competition on different lattices.

Findings

Doping induces four inequivalent Hamiltonian families on the triangular lattice.

The symmetry enables duality between bosonic and fermionic hole descriptions.

Various phases such as superfluidity and phase separation are analyzed within this framework.

Abstract

We prove a "statistical transmutation" symmetry of doped quantum dimer models on the square, triangular and kagome lattices: the energy spectrum is invariant under a simultaneous change of statistics (i.e. bosonic into fermionic or vice-versa) of the holes and of the signs of all the dimer resonance loops. This exact transformation enables to define duality equivalence between doped quantum dimer Hamiltonians, and provides the analytic framework to analyze dynamical statistical transmutations. We investigate numerically the doping of the triangular quantum dimer model, with special focus on the topological Z2 dimer liquid. Doping leads to four (instead of two for the square lattice) inequivalent families of Hamiltonians. Competition between phase separation, superfluidity, supersolidity and fermionic phases is investigated in the four families.