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

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.

arXiv comment10 pages, 12 figures

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• Revisiting the Kitaev material candidacy of Ir4+ double perovskite iridates
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• Comprehensive study of the global phase diagram in the triangular $J$-$K$-$\Gamma$ model
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• Quantum selection of order and dynamic properties of Kitaev-Heisenberg ferromagnet on a triangular lattice
• Coupled spin-1/2 antiferromagnetic chain Cs${}_2$LiRuCl${}_6$ with partially disordered crystal lattice
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