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.
Highlights
Calculations in condensed matter theory must generally bridge two different gaps
There are models which are both physically relevant and for which exact calculations are possible. These have been important in the development of modern condensed matter physics, especially where they have been used to establish the theoretical possibility of novel phenomena or phases of matter
The combination of the large ground-state degeneracy and the coexistence of infinite-range and algebraic correlations suggest an analogy with the phenomenon of “magnetic moment fragmentation” [15,16,17,18,19,21,22,23] but the case here is distinguished by the fact that it occurs in the exact ground states of a quantum model
Summary
Calculations in condensed matter theory must generally bridge two different gaps. The first is the gap between model and experiment: any model simple enough to be successfully studied cannot capture every aspect of a real many-body system, though we hope to capture the most important and interesting ones. (denoted as the XXZ0 point [11]) the model has a set of exact, degenerate, ground states, the number of which grows exponentially with system size These ground states can be written as simple product states, despite the fact that the Hamiltonian is composed of noncommuting terms and that general excited eigenstates are entangled. We further show that despite having an extensive number of undetermined degrees of freedom, the ground states possess infinite-range correlations of some spin components, coexisting with algebraic correlations This is qualitatively reminiscent of the phenomenon of “magnetic moment fragmentation” [15,16,17] studied in both kagome [18,19,20] and pyrochlore [15,21,22,23] systems, but is remarkable because it occurs in the exact ground states of a quantum model. Generate ground states on the lattice by tiling single-triangle ground states across the system
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