Uniqueness of states satisfying Kubo–Martin–Schwinger boundary conditions in the case of one-dimensional quantum spin systems with finite-range potential

For one-dimensional quantum spin systems with finite-range potential Araki [1] has constructed a state that is the thermodynamic limit of Gibbs states in finite volumes and satisfies the Kubo–Martin–Schwinger boundary conditions. In the present paper it is shown that for the systems considered by Araki a state satisfying the Kubo–Martin–Schwinger boundary conditions is unique. This result means that all one-dimensional quantum spin systems with finite-range potential are single-phase.