Tensor network wave function of S=1 Kitaev spin liquids

Abstract

The spin-1/2 Kitaev model offers the exactly solvable example of quantum spin liquids. Possible material realizations of the spin-1/2 Kitaev systems and the prospect of using the Majorana fermion excitations for quantum computations have revolutionized quantum spin liquids research. Recently it has been suggested that higher-spin, especially spin-1, Kitaev exchange interactions can be realized in a variety of materials. Numerical computations on small clusters indicate that the ground state of the spin-1 Kitaev model may also be a quantum spin liquid. On the other hand, the nature of the ground state remains elusive since the spin-1 model is not exactly solvable in contrast to the spin-1/2 model. In this work, using the quantum-entanglement based tensor network approach, we construct an explicit ground-state wave function for the spin-1 Kitaev model, which is written only in terms of physical spin operators. We establish the existence of distinct topological sectors on a 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 spin-1 Kitaev model is a gapped quantum spin liquid with Z2 gauge structure and Abelian quasiparticles. We explain the subtle differences between the spin-1/2 and spin-1 Kitaev quantum spin liquids.Received 8 January 2020Revised 19 May 2020Accepted 24 June 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.033318Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasClassical statistical mechanicsQuantum spin liquidTensor network renormalizationPhysical SystemsQuantum spin modelsTechniquesKitaev modelTensor network methodsCondensed Matter, Materials & Applied Physics