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We study the Kitaev-Heisenberg-$\Gamma$ model with antiferromagnetic Kitaevexchanges in the strong anisotropic (toric code) limit to understand the phasesand the intervening phase transitions between the gapped $Z_2$ quantum spinliquid and the spin-ordered (in the Heisenberg limit) as well as paramagneticphases (in the pseudo-dipolar, $\Gamma$, limit). We find that the paramagneticphase obtained in the large $\Gamma$ limit has no topological entanglemententropy and is proximate to a gapless critical point of a system described byan equal superposition of differently oriented stacked one-dimensional$Z_2\times Z_2$ symmetry protected topological phases. Using a combination ofexact diagonalization calculations and field-theoretic analysis we map out thephases and phase transitions to reveal the complete phase diagram as a functionof the Heisenberg, the Kitaev, and the pseudo-dipolar interactions. Our workshows a rich plethora of unconventional phases and phase transitions andprovides a comprehensive understanding of the physics of anisotropicKitaev-Heisenberg-$\Gamma$ systems along with our recent paper [Phys. Rev. B102, 235124 (2020)] where the ferromagnetic Kitaev exchange was studied.

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