Phase diagram of the fully frustrated transverse-field Ising model on the honeycomb lattice

TL;DR

This paper explores the phase diagram of a fully frustrated transverse-field Ising model on the honeycomb lattice, revealing multiple symmetry-breaking phases and their quantum modifications, with implications for quantum dimer models.

Contribution

It provides a detailed classical and semiclassical analysis of the phase diagram, identifying new phases and their quantum stability in the model.

Findings

Multiple phases break translational symmetry.

Plaquette phase extends to zero field for spin 1/2.

Quantum fluctuations favor the plaquette phase at low fields.

Abstract

Motivated by the current interest in the quantum dimer model on the triangular lattice, we investigate the phase diagram of the closely related fully-frustrated transverse field Ising model on the honeycomb lattice using classical and semi-classical approximations. We show that, in addition to the fully polarized phase at large field, the classical model possesses a multitude of phases that break the translational symmetry which in the dimer language, correspond to a plaquette phase and a columnar phase separated by an infinite cascade of mixed phases. The modification of the phase diagram by quantum fluctuations has been investigated in the context of linear spin-wave theory. The extrapolation of the semiclassical energies suggests that the plaquette phase extends down to zero field for spin 1/2, in agreement with the $\sqrt{12}\times\sqrt{12}$ phase of the quantum dimer model on the triangular lattice with only kinetic energy.