Insights into the Anisotropic Spin-$S$ Kitaev Chain

TL;DR

This paper investigates the low-energy properties and thermodynamics of anisotropic spin-$S$ Kitaev chains, revealing distinct behaviors for integer and half-integer spins and providing insights into their phase structure and excitations.

Contribution

It derives an effective low-energy Hamiltonian for the anisotropic spin-$S$ Kitaev chain and analyzes differences between integer and half-integer spins, advancing understanding of their quantum phases.

Findings

Half-integer spins exhibit a trivial effective model with non-local symmetry.

Integer spins show interactions among flux degrees of freedom, leading to a unique ground state.

Predictions for low-energy excitations and thermodynamics are made for integer spins.

Abstract

Recently there has been a renewed interest in properties of the higher-spin Kitaev models, especially their low-dimensional analogues with additional interactions. These quasi-1D systems exhibit rich phase diagrams with symmetry-protected topological phases, Luttinger liquids, hidden order, and higher-rank magnetism. However, the nature of the pure spin-$S$ Kitaev chains are not yet fully understood. Earlier works found a unique ground state with short-ranged correlations for $S = 1$, and an intriguing double-peak structure in the heat capacity associated with an entropy plateau. To understand the low-energy excitations and thermodynamics for general $S$ we study the anisotropic spin-$S$ Kitaev chain. Starting from the dimerized limit we derive an effective low-energy Hamiltonian at finite anisotropy. For half-integer spins we find a trivial effective model, reflecting a non-local symmetry protecting the degeneracy, while for integer $S$ we find interactions among the flux degrees of freedom that select a unique ground state. The effective model for integer spins is used to predict the low-energy excitations and thermodynamics, and we make a comparison with the semiclassical limit through linear spin wave theory. Finally, we speculate on the nature of the isotropic limit.