Quantum phase transitions in the spin-1 Kitaev-Heisenberg chain

TL;DR

This paper investigates the phase diagram of the spin-1 Kitaev-Heisenberg chain using numerical methods, revealing various ordered phases, a quantum spin liquid, and a topological Haldane phase.

Contribution

It provides the first detailed numerical analysis of the $S=1$ Kitaev-Heisenberg model, identifying its ground states and phase transitions.

Findings

Identified ferromagnetic and left-left-right-right ordered phases for $J<0$

Found a quantum spin liquid near the Kitaev limit

Discovered a topological Haldane phase for $J>0

Abstract

Recently, it has been proposed that higher-spin analogues of the Kitaev interactions $K>0$ may also occur in a number of materials with strong Hund's and spin-orbit coupling. In this work, we use Lanczos diagonalization and density matrix renormalization group methods to investigate numerically the $S=1$ Kitaev-Heisenberg model. The ground-state phase diagram and quantum phase transitions are investigated by employing local and nonlocal spin correlations. We identified two ordered phases at negative Heisenberg coupling $J<0$: a~ferromagnetic phase with $\langle S_i^zS_{i+1}^z\rangle>0$ and an intermediate left-left-right-right phase with $\langle S_i^xS_{i+1}^x\rangle\neq 0$. A~quantum spin liquid is stable near the Kitaev limit, while a topological Haldane phase is found for $J>0$.