Ground-state phase diagram of the S=1/2 Heisenberg-Γ model on a honeycomb lattice.

We investigate the ground-state phase diagram of the S=1/2 Heisenberg-Γ model on a honeycomb lattice by utilizing several numerical methods, such as dimer series expansion, the numerical exact-diagonalization method and the density-matrix-renormalization-group method. In this study, we focus on the effect of the anisotropic interaction; we investigate the ground state from the isolated dimer limit to the spin-chain limit by changing the coupling constants. From the results obtained, we find that in the spin-chain limit, there are three kinds of states, namely the Tomonaga-Luttinger liquid state and two magnetically long-range-ordered states. These three states become two-dimensional long-range ordered states by adding the infinitesimal interchain interaction. Starting from the isolated dimer limit, we find that a triplet dimer phase can survive up to the isotopically interacting case in a large part of parameter region where the Heisenberg and Γ interactions are ferromagnetic and antiferromagnetic, respectively. Otherwise, a phase transition to a magnetically ordered phase occurs before the isotopically interacting model. This indicates that the quantum spin liquid expected in the Γ model is unstable against the anisotropy of the interactions.