Chiral Soliton Phases in Kitaev Spin Chains*

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 Kitaev spin chains with alternating x- and y-bond Ising interactions. Previous studies have focused on a transverse field, h_z, and reported a direct transition to the polarized state. Here, we investigate phase diagram with arbitrary angle of two longitudinal fields, h_x and h_y.  For a magnetic field applied along the diagonal, h_x=h_y, the chain remains gapless up to a critical field h^c1.  Surprisingly, above h^c1 it enters an unusual intermediate phase before reaching the polarized state at h^c2.  This phase is characterized by a staggered vector chirality and for periodic boundary conditions, a two-fold degeneracy with a finite gap.  For open boundary systems the ground-state exhibits a single soliton, lowering the energy, and gapless excitations.  However, the corresponding anti-soliton raises the energy sufficiently that a gap appears for soliton and anti-soliton  pairs in periodic systems.  We discuss an intuitive variational picture describing the soliton phase.