We study soliton sectors of the XY model by using known results and methods about its ground states. In the regions of parameters for which ground states are not unique, we show that (1) there are two soliton sectors depending on parameters of the model analytically in a well-defined sense, (2) the only sectors with “finite energy” are ground state and soliton sectors, and (3) the sudden appearance of additional ground states at a pair of specific values of parameters (despite analytic dependence of other ground states on parameters at those specific values), which were found in earlier study of ground states, can be understood as the degeneracy of one particle energy in the soliton sector (which has a continuous spectrum at other values of parameters) to a single point spectrum with infinite multiplicity at the specific values of parameters.
Analytic dependence on parameters for Evans' approximated Weak KAM solutions
