Phases and Quantum Phase Transitions in Anisotropic Antiferromagnetic Kitaev-Heisenberg-$\Gamma$ magnet

TL;DR

This paper investigates the complex phase diagram of the anisotropic Kitaev-Heisenberg-$\Gamma$ model, revealing various unconventional phases and phase transitions between quantum spin liquids, spin-ordered, and paramagnetic states using numerical and theoretical methods.

Contribution

It provides a comprehensive analysis of the phases and phase transitions in the anisotropic Kitaev-Heisenberg-$\Gamma$ model, including the nature of the paramagnetic phase and its relation to topological phases.

Findings

Identification of the paramagnetic phase with no topological entanglement entropy.

Mapping of the complete phase diagram as a function of interaction parameters.

Discovery of a gapless critical point related to stacked $Z_2 imes Z_2$ SPT phases.

Abstract

We study the Kitaev-Heisenberg-$\Gamma$ model with antiferromagnetic Kitaev exchanges in the strong anisotropic (toric code) limit to understand the phases and the intervening phase transitions between the gapped $Z_2$ quantum spin liquid and the spin-ordered (in the Heisenberg limit) as well as paramagnetic phases (in the pseudo-dipolar, $\Gamma$, limit). We find that the paramagnetic phase obtained in the large $\Gamma$ limit has no topological entanglement entropy and is proximate to a gapless critical point of a system described by an equal superposition of differently oriented stacked one-dimensional $Z_2\times Z_2$ symmetry protected topological phases. Using a combination of exact diagonalization calculations and field-theoretic analysis we map out the phases and phase transitions to reveal the complete phase diagram as a function of the Heisenberg, the Kitaev, and the pseudo-dipolar interactions. Our work shows a rich plethora of unconventional phases and phase transitions and provides a comprehensive understanding of the physics of anisotropic Kitaev-Heisenberg-$\Gamma$ systems along with our recent paper [Phys. Rev. B 102, 235124 (2020)] where the ferromagnetic Kitaev exchange was studied.