Field-induced chiral soliton phase in the Kitaev spin chain

The bond-dependent Ising interaction present in the Kitaev model has attracted considerable attention. The appearance of an unexpected intermediate phase under a magnetic field is particularly intriguing, and one may wonder if a similar phase occurs in the Kitaev spin chain with alternating x- and y-bond Ising interactions. Previous studies have focused on a transverse field hz and reported a direct transition to the polarized state. Here, we investigate phases with an arbitrary angle of two longitudinal fields, hx and hy. For a magnetic field applied along the diagonal, hx=hy, the chain remains gapless up to a critical field hxyc1. Surprisingly, above hxyc1 it enters an unusual intermediate phase before reaching the polarized state at hxyc2. This phase is characterized by a staggered vector chirality and for periodic boundary conditions, a twofold degeneracy with a finite gap. For open boundary systems the ground state exhibits a single soliton, lowering the energy, and in-gap excitations. However, the corresponding antisoliton raises the energy sufficiently that a gap appears for soliton and antisoliton pairs in periodic systems. An intuitive variational picture is developed describing the soliton phase. A phase descending from the intermediate field phase is also identified in the two-leg Kitaev ladder.