Ground-state phase diagram of anisotropically interacting Heisenberg- ? models on a honeycomb lattice

In this paper, we investigate the ground-state phase diagram of $S=1/2$ Heisenberg-$\mathrm{\ensuremath{\Gamma}}$ model on a honeycomb lattice by dimer series expansion and exact diagonalization. We focus effects anisotropy interactions; tuning coupling constants, system changes between isolated spin-chain models. find that, in limit, there are three kinds states: A Tomonaga-Luttinger liquid two magnetically long-range-ordered states. All states become two-dimensional infinitesimal interchain interaction except for case where Heisenberg is much weaker than off-diagonal symmetric $(\mathrm{\ensuremath{\Gamma}})$ interaction. Starting from triplet survives up to isotropically interacting large part $\mathrm{\ensuremath{\Gamma}}$ interactions ferromagnetic antiferromagnetic, respectively. Otherwise, transition ordered occurs before becomes isotropic. This indicates that quantum spin proposed [A. Catuneanu et al., npj Quantum Mater. 3, 23 (2018)] unstable against interactions.