Tensor network wavefunction of $S=1$ Kitaev spin liquids

TL;DR

This paper constructs a tensor network wavefunction for the S=1 Kitaev model, providing insights into its topological nature and suggesting it is a gapped quantum spin liquid with Z2 gauge structure.

Contribution

It introduces a tensor network approach to study the S=1 Kitaev model, revealing its topological sectors and characterizing its quantum spin liquid ground state.

Findings

Ground state is a gapped quantum spin liquid

Existence of topological sectors on torus

Ground state has Z2 gauge structure and Abelian quasiparticles

Abstract

Recently there has been a great interest in understanding quantum spin liquid phases with varying spin magnitude, partly due to possible material realizations. A number of recent numerical computations suggest that the ground state of the S=1 Kitaev model may be a quantum spin liquid in analogy to the renowned $S$=$1/2$ model. On the other hand, the nature of the ground state remains elusive since the $S$=$1$ model is not exactly solvable in contrast to the $S$=$1/2$ model. In this work, we construct a tensor network ground state wavefunction for the S=1 Kitaev model, which is explicitly written in terms of physical spin operators. We explain how this class of wavefunctions can be successfully used for variational computations and compare the outcomes to known results on finite size systems. We establish the existence of distinct topological sectors on torus by constructing the minimally entangled states in the degenerate ground state manifold and evaluating topological entanglement entropy. Our results suggest that the ground state of the S=1 Kitaev model is a gapped quantum spin liquid with Z2 gauge structure and Abelian quasiparticles.