Field induced phases of the Kitaev-Γ ladder

The Kitaev spin model on honeycomb lattice has attracted significant attention since the emergence of α-RuCl₃ as a promising Kitaev spin liquid candidate in the presence of a magnetic field. While the mechanism of such a field-induced Kitaev spin liquid is not yet fully understood, theoretical studies have shown that the bond-dependent Γ and Kitaev interactions are equally significant in α-RuCl₃ leading to a minimal spin-½ Kitaev-Γ (KG) model. In the pure antiferromagnetic Kitaev limit, previous numerical studies have shown gapless states for a range of intermediate field strengths, leading to the suggestion of a U(1) spin liquid phase. However, a possibility of incommensurate magnetic orderings cannot be excluded. Employing large-scale numerical techniques, we study the KG model in a two-leg ladder system in the presence of a magnetic field for the entire phase space of the KG model, finding both disordered and incommensurate ordered phases near the antiferromagnetic Kitaev region. We discuss the models limitations and relation to the two-dimensional honeycomb lattice.