Spin-1 Kitaev-Heisenberg model on a two-dimensional honeycomb lattice

TL;DR

This study explores the phase diagram of the spin-1 Kitaev-Heisenberg model on a honeycomb lattice, revealing gapless spin liquid phases and contrasting them with the spin-1/2 case.

Contribution

It provides the first detailed numerical analysis of the spin-1 Kitaev-Heisenberg model, identifying its phase diagram and the nature of its spin liquid phases.

Findings

Identified two spin liquid phases and four symmetry broken phases.

Found that spin liquid phases are gapless with short-range correlations.

Compared spin-1 and spin-1/2 cases, noting differences in gapless modes.

Abstract

We study the Kitaev-Heisenberg model with spin-1 local degree of freedom on a two-dimensional honeycomb lattice numerically by density matrix renormalization group method. By tuning the relative value of the Kitaev and Heisenberg exchange couplings, we obtain the whole phase diagram with two spin liquid phases and four symmetry broken phases. We identify that the spin liquid phases are gapless by calculating the central charge at the pure Kitaev points without Heisenberg interaction. Comparing to its spin-1/2 counterpart, the position and number of gapless modes of the spin-1 case are quite different. Due to the approximate $Z_2$ local conservations, the expectation value of Wilson loop operator measuring the flux of each plaquette stays near to 1, and the static spin-spin correlations remain short-range in the entire spin liquid phases.