Recently considerable excitement has arisen due to the experimental observation of a field-induced spin liquid phase in the compound $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. However, the nature of this putative spin liquid phase and the relevant microscopic model Hamiltonian remain still unclear. In this work, we address these questions by performing large-scale numerical simulations of a generalized Kitaev-Heisenberg model proposed to describe the physics of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. While an intermediate phase does not appear for in-plane magnetic fields, our results strongly suggest that a stable intermediate spin liquid phase, sandwiched between a magnetically ordered phase at low fields and a high-field polarized phase, can be induced by out-of-plane magnetic fields. Moreover, we show that this field-induced spin liquid phase can be smoothly connected to a spin liquid possessing a spinon Fermi surface as proposed recently for the Kitaev model. The relevance of our results to $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ is also discussed.
We study the extent of the spin liquid phases in the Kitaev-Heisenberg model using infinite projected entangled-pair states tensor network ansatz wave functions directly in the thermodynamic limit. To assess the accuracy of the ansatz wave functions, we perform benchmarks against exact results for the Kitaev model and find very good agreement for various observables. In the case of the Kitaev-Heisenberg model, we confirm the existence of six different phases: N\'eel, stripy, ferromagnetic, zigzag, and two spin liquid phases. We find finite extents for both spin liquid phases and discontinuous phase transitions connecting them to symmetry-broken phases.
Quantum spin models with spatially dependent interactions, known as compass models, play an important role in study of frustrated quantum magnetism and Mott insulators with orbital degrees of freedom. One example is Kitaev model on honeycomb lattice with spin liquid ground states and anyonic excitations. It is highly desirable to go beyond this exactly solvable limit by generalizing Kitaev model to connect with specific materials or other known models. A conventional way to achieve this is through hybridization with other models. For example, Kitaev-Heisenberg model was proposed to describe iridates. Here we pursue an alternative direction and propose a new dubbed the tripod model, which contains a continuum of compass-type models. It smoothly interpolates Ising Kitaev and quantum
120∘ model by tuning a single parameter
θ′, angle between three legs of a tripod in spin space. Not only does tripod model establish a natural connection between three paradigmatic models, but it also enables study of quantum phase transitions between them. We solve this model numerically by tensor networks in thermodynamic limit and find a spin-disordered (spin liquid) phase between an antiferromagnetic phase and a dimer phase. Our results unambiguously establish long-range order of geometrically frustrated
120∘ model and provide an intuitive picture for phase transition between spin-liquid phase and dimer phase. The tripod model proposed here could be realized in cold atoms experiments by introducing non-Abelian artificial gauge fields for fermionic Hubbard model.