Phase diagram of the Kitaev-Γ model on the honeycomb lattice*

Spin-1/2 K-Γ model emerges as the minimal description for many Kitaev materials. Despite much effort, the parameter region of K<0 and Γ>0, which is particularly relevant to real materials, remains enigmatic in both quantum and classical models. Hence, in this work, we focus on studying this parameter region both classically and quantum-mechanically. In the classical limit, we employ Monte Carlo simulations on a series of elongated clusters to show the existence of multisublattice states characterized by scalar chirality. In the quantum limit, we use linked-cluser expansions to show that the quantum ground state can be understood in terms of particular dimer coverings, in a large part of the studied region. We also study the quantum phase diagram with exact diagonalization on the clusters with different sizes and shapes, and show that the results from linked-cluster expansions and from exact diagonalization are consist.