Quantum dimer models and effective Hamiltonians on the pyrochlore lattice

TL;DR

This paper explores a large-N deformation of the pyrochlore Heisenberg antiferromagnet, leading to a solvable quantum dimer model that reveals symmetry-breaking phases and offers new insights into the SU(2) problem and classical dimer models.

Contribution

It introduces a large-N approach to the pyrochlore Heisenberg model, providing a solvable quantum dimer model and analyzing symmetry-breaking phases and effective Hamiltonians.

Findings

Ground state breaks inversion symmetry without translational symmetry breaking.

Effective Hamiltonian describes dimer potential energies with translational symmetry breaking.

Mean-field states correspond to maximally flippable dimer configurations.

Abstract

We study a large-N deformation of the S=1/2 pyrochlore Heisenberg antiferromagnet which leads to a soluble quantum dimer model at leading non-trivial order. In this limit, the ground state manifold -- while extensively degenerate -- breaks the inversion symmetry of the lattice, which implies a finite temperature Ising transition without translational symmetry breaking. At lower temperatures and further in the 1/N expansion, we discuss an effective Hamiltonian within the degenerate manifold, which has a transparent physical interpretation as representing dimer potential energies. We find mean-field ground states of the effective Hamiltonian which exhibit translational symmetry breaking. The entire scenario offers a new perspective on previous treatments of the SU(2) problem not controlled by a small parameter, in particular showing that a mean-field state considered previously encodes the physics of a maximally flippable dimer configuration. We also comment on the difficulties of extending our results to the SU(2) case, and note implications for classical dimer models.