Exactly solvable spin-1/2 XYZ models with highly-degenerate, partially ordered, ground states

TL;DR

This paper extends an exactly solvable, highly degenerate ground state model from the XXZ to a more general XYZ model on kagome-like lattices, revealing partially ordered states with mixed properties.

Contribution

It generalizes the exactly solvable kagome XXZ model to an XYZ model, maintaining degeneracy and three-coloring solutions, and introduces partially ordered ground states.

Findings

Ground states exhibit partial order with coexistence of correlations and degeneracy.

Extension of the model preserves macroscopic degeneracy and three-coloring structure.

Proposes a new class of models with mixed ordered and spin liquid-like properties.

Abstract

Exactly solvable models play a special role in Condensed Matter physics, serving as secure theoretical starting points for investigation of new phenomena. Changlani et al. [Phys. Rev. Lett. 120, 117202 (2018)] have discovered a limit of the XXZ model for $S=1/2$ spins on the kagome lattice, which is not only exactly solvable, but features a huge degeneracy of exact ground states corresponding to solutions of a three-coloring problem. This special point of the model was proposed as a parent for multiple phases in the wider phase diagram, including quantum spin liquids. Here, we show that the construction of Changlani et al. can be extended to more general forms of anisotropic exchange interaction, finding a line of parameter space in an XYZ model which maintains both the macroscopic degeneracy and the three-coloring structure of solutions. We show that the ground states along this line are partially ordered, in the sense that infinite-range correlations of some spin components coexist with a macroscopic number of undetermined degrees of freedom. We therefore propose the exactly solvable limit of the XYZ model on corner-sharing triangle-based lattices as a tractable starting point for discovery of quantum spin systems which mix ordered and spin liquid-like properties.