Islands of Chiral Solitons in Integer Spin Kitaev Chains

An intriguing chiral soliton phase has recently been identified in the $S$=1/2 Kitaev spin chain. Here we show that for $S$=1,2,3,4,5 an analogous phase can be identified, but contrary to the $S$=1/2 case the chiral soliton phases appear as islands within the sea of the polarized phase. In fact, a small field applied in a general direction will adiabatically connect the integer spin Kitaev chain to the polarized phase. Only at sizable intermediate fields along symmetry directions does the soliton phase appear centered around the special point $h^\star_x$=$h^\star_y$=$S$ where two exact product ground-states can be identified. The large $S$ limit can be understood from a semi-classical analysis, and variational calculations provide a detailed picture of the $S$=1 soliton phase. Under open boundary conditions, the chain has a single soliton in the ground-state which can be excited, leading to a proliferation of in-gap states. In contrast, even length periodic chains exhibit a gap above a twice degenerate ground-state. The presence of solitons leaves a distinct imprint on the low temperature specific heat.