A continuum of compass spin models on the honeycomb lattice

TL;DR

This paper introduces the tripod model, a continuum of compass spin models on the honeycomb lattice, unifying key models and enabling the exploration of their quantum phase transitions and phases.

Contribution

It proposes the tripod model that interpolates between Ising, Kitaev, and 120° models, providing a unified framework for studying their phase diagram and transitions.

Findings

Ground state of the 120° model exhibits long-range dimer order.

An extended spin-liquid phase exists between dimer and antiferromagnetic phases.

The model's phase diagram was numerically obtained using tensor networks.

Abstract

Quantum spin models with spatially dependent interactions, known as compass models, play an important role in the study of frustrated quantum magnetism. One example is the Kitaev model on the honeycomb lattice with spin-liquid ground states and anyonic excitations. Another example is the geometrically frustrated quantum $120^\circ$ model on the same lattice whose ground state has not been unambiguously established. To generalize the Kitaev model beyond the exactly solvable limit and connect it with other compass models, we propose a new model, dubbed "the tripod model", which contains a continuum of compass-type models. It smoothly interpolates the Ising model, the Kitaev model, and the quantum $120^\circ$ model by tuning a single parameter $\theta'$, the angle between the three legs of a tripod in the spin space. Hence it not only unifies three paradigmatic spin models, but also enables the study of their quantum phase transitions. We obtain the phase diagram of the tripod model numerically by tensor networks in the thermodynamic limit. We show that the ground state of the quantum $120^\circ$ model has long-range dimer order. Moreover, we find an extended spin-disordered (spin-liquid) phase between the dimer phase and an antiferromagnetic phase. The unification and solution of a continuum of frustrated spin models as outline here may be useful to exploring new domains of other quantum spin or orbital models.