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

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.

33 pages, 29 figures, Companion paper to arXiv:2006.10081

References in corpus (9)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• "Deconfined" quantum critical points
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• Exact results for spin dynamics and fractionization in the Kitaev Model
• Robustness of a perturbed topological phase
• Non-coplanar and counter-rotating incommensurate magnetic order stabilized by Kitaev interactions in $\gamma$-Li2IrO3
• Global phase diagrams of frustrated quantum antiferromagnets in two dimensions: doubled Chern-Simons theory
• Fate of the cluster state on the square lattice in a magnetic field
• Phases and phase transitions of a perturbed Kekulé-Kitaev model