Field-induced chiral soliton phase in the Kitaev spin chain

Abstract

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 h_{z} and reported a direct transition to the polarized state. Here, we investigate phases with an 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_{xy}^{c_{1}}. Surprisingly, above h_{xy}^{c1} it enters an unusual intermediate phase before reaching the polarized state at h_{xy}^{c_{2}}. 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.