Density-Matrix Renormalization Group Study of Kitaev--Heisenberg Model on a Triangular Lattice

TL;DR

This study uses the density-matrix renormalization group method to map out the complex phase diagram of the Kitaev--Heisenberg model on a triangular lattice, revealing multiple phases and their entanglement properties.

Contribution

It provides the first detailed phase diagram of the Kitaev--Heisenberg model on a triangular lattice using DMRG, identifying novel phases and analyzing entanglement features at phase boundaries.

Findings

Identified multiple phases including AFM, vortex, nematic, and ferromagnetic phases.

Discovered first-order phase transitions with discontinuous changes in spin correlations.

Found that entanglement entropy and Schmidt gap effectively indicate phase boundaries in this model.

Abstract

We study the Kitaev--Heisenberg model on a triangular lattice by using the two-dimensional density-matrix renormalization group method. Calculating the ground-state energy and spin structure factors, we obtain a ground-state phase diagram of the Kitaev--Heisenberg model. As suggested by previous studies, we find a 120$^\circ$ antiferromagnetic (AFM) phase, a $\mathbb{Z}_2$-vortex crystal phase, a nematic phase, a dual $\mathbb{Z}_2$-vortex crystal phase (the dual counterpart of the $\mathbb{Z}_2$-vortex crystal phase), a $\mathbb{Z}_6$ ferromagnetic phase, and a dual ferromagnetic phase (the dual counterpart of the $\mathbb{Z}_6 $ ferromagnetic phase). Spin correlations discontinuously change at phase boundaries because of first-order phase transitions. We also study the relation among the von Neumann entanglement entropy, entanglement spectrum, and phase transitions of the model. We find that the Schmidt gap closes at phase boundaries and thus the entanglement entropy clearly changes as well. This is different from the Kitaev--Heisenberg model on a honeycomb lattice, where the Schmidt gap and entanglement entropy are not necessarily a good measure of phase transitions.