Excitation spectrum of spin-1 Kitaev spin liquids

TL;DR

This paper investigates the excitation spectrum of the spin-1 Kitaev model using tensor network methods, revealing a $ ext{Z}_2$ spin liquid phase with dispersive charge anyon excitations, contrasting with the spin-1/2 case.

Contribution

It introduces a tensor network approach to analyze the spin-1 Kitaev model's excitations and identifies the nature of its charge anyon excitations and their dispersion.

Findings

Ground state is a $ ext{Z}_2$ spin liquid.

Dispersive charge anyon excitations are found.

Excitation minima located at specific momentum points.

Abstract

We study the excitation spectrum of the spin-1 Kitaev model using the symmetric tensor network. By evaluating the virtual order parameters defined on the virtual Hilbert space in the tensor network formalism, we confirm the ground state is in a $\mathbb{Z}_2$ spin liquid phase. Using the correspondence between the transfer matrix spectrum and low-lying excitations, we find that contrary to the dispersive Majorana excitation in the spin-1/2 case, the isotropic spin-1 Kitaev model has a dispersive charge anyon excitation. Bottom of the gapped single-particle charge excitations are found at $\mathbf{K}, \mathbf{K}'=(\pm2\pi/3, \mp 2\pi/3)$, with a corresponding correlation length of $\xi \approx 6.7$ unit cells. The lower edge of the two-particle continuum, which is closely related to the dynamical structure factor measured in inelastic neutron scattering experiments, is obtained by extracting the excitations in the vacuum superselection sector in the anyon theory language