Competing orders II: the doped quantum dimer model

TL;DR

This paper explores the phases of doped quantum antiferromagnets on a square lattice, extending the quantum dimer model to include fermionic excitations, and analyzes the interplay of various orders and excitations relevant to high-temperature superconductivity.

Contribution

It introduces an extended quantum dimer model with fermionic excitations and connects gauge theory descriptions to experimental phenomena in doped antiferromagnets.

Findings

Duality mapping of the dimer model captures gauge fluctuation effects.

The dual vortex theory shares symmetries with previous boson dualities.

A phenomenological model for S=1 excitations relates to neutron scattering data.

Abstract

We study the phases of doped spin S=1/2 quantum antiferromagnets on the square lattice, as they evolve from paramagnetic Mott insulators with valence bond solid (VBS) order at zero doping, to superconductors at moderate doping. The interplay between density wave/VBS order and superconductivity is efficiently described by the quantum dimer model, which acts as an effective theory for the total spin S=0 sector. We extend the dimer model to include fermionic S=1/2 excitations, and show that its mean-field, static gauge field saddle points have projective symmetries (PSGs) similar to those of `slave' particle U(1) and SU(2) gauge theories. We account for the non-perturbative effects of gauge fluctuations by a duality mapping of the S=0 dimer model. The dual theory of vortices has a PSG identical to that found in a previous paper (L. Balents et al., cond-mat/0408329) by a duality analysis of bosons on the square lattice. The previous theory therefore also describes fluctuations across superconducting, supersolid and Mott insulating phases of the present electronic model. Finally, with the aim of describing neutron scattering experiments, we present a phenomenological model for collective S=1 excitations and their coupling to superflow and density wave fluctuations.