Density-Matrix Renormalization Group Study of Extended Kitaev-Heisenberg Model

TL;DR

This study uses density-matrix renormalization group methods to explore an extended Kitaev-Heisenberg model, revealing various magnetic phases and entanglement properties around the spin-liquid phase.

Contribution

It provides a detailed phase diagram of the extended model and analyzes entanglement spectra, highlighting features of phase transitions and the nature of different phases.

Findings

Identification of multiple magnetic phases including zigzag, ferromagnetic, and incommensurate phases.

Entanglement spectrum analysis shows degeneracy in the spin-liquid phase and non-degeneracy in ordered phases.

The Schmidt gap signals phase boundaries near the spin-liquid phase but not between all magnetic phases.

Abstract

We study an extended Kitaev-Heisenberg model including additional anisotropic couplings by using two-dimensional density-matrix renormalization group method. Calculating the gound-state energy, entanglement entropy, and spin-spin correlation functions, we make a phase diagram of the extended Kitaev-Heisenberg model around spin-liquid phase. We find a zigzag antiferromagnetic phase, a ferromagnetic phase, a 120-degree antiferromagnetic phase, and two kinds of incommensurate phases around the Kitaev spin-liquid phase. Furthermore, we study the entanglement spectrum of the model and find that entanglement levels in the Kitaev spin-liquid phase are degenerate forming pairs but those in the magnetically ordered phases are non-degenerate. The Schmidt gap defined as the energy difference between the lowest two levels changes at the phase boundary adjacent to the Kitaev spin-liquid phase. However, we find that phase boundaries between magnetically ordered phases do not necessarily agree with the change of the Schmidt gap.