Comprehensive study of the global phase diagram in the triangular $J$$K$$\Gamma$ model
Abstract
The celebrated Kitaev honeycomb model provides an analytically tractable example with an exact quantum spin liquid ground state. While in real materials, other types of interactions besides the Kitaev coupling ($K$) are present, such as the Heisenberg ($J$) and symmetric offdiagonal ($\Gamma$) terms, and these interactions can also be generalized to a triangular lattice. Here, we carry out a comprehensive study of the $J$$K$$\Gamma$ model on the triangular lattice covering the full parameters region, using the combination of the exact diagonalization, classical Monte Carlo and analytic methods. In the HK limit ($\Gamma=0$), we find five quantum phases which are quite similar to their classical counterparts. Among them, the stripeA and dual Néel phase are robust against the $\Gamma$ term, in particular the stripeA extends to the region connecting the $K=1$ and $K=1$ for $\Gamma<0$. Though the 120$^\circ$ Néel phase also extends to a finite $\Gamma$, its region has been largely reduced compared to the previous classical result. Interestingly, the ferromagnetic (dubbed as FMA) phase and the stripeB phase are unstable in response to an infinitesimal $\Gamma$ interaction. Moreover, we find five new phases for $\Gamma\ne 0$ which are elaborated by both the quantum and classical numerical methods. Part of the space previously identified as 120$^\circ$ Néel phase in the classical study is found to give way to the modulated stripe phase. Depending on the sign of the $\Gamma$, the FMA phase transits into the FMB ($\Gamma>0$) and FMC ($\Gamma<0$) phase with different spin orientations, and the stripeB phase transits into the stripeC ($\Gamma>0$) and stripeA ($\Gamma<0$). Around the positive $\Gamma$ point, due to the interplay of the Heisenberg, Kiatev and $\Gamma$ interactions, we find a possible quantum spin liquid with a continuum in spin excitations.
 Publication:

arXiv eprints
 Pub Date:
 August 2020
 DOI:
 10.48550/arXiv.2008.10972
 arXiv:
 arXiv:2008.10972
 Bibcode:
 2020arXiv200810972W
 Keywords:

 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 12 pages, 12 figures