Markovian KMS-states for one-dimensional spin chains

We characterize a class of quantum Markov states in terms of a locality pro perty of their modular automorphism group or, equivalently, of their phi-co nditional expectations and we give an explicit description of the structure of these states. This study is meant as a starting point for the investiga tion of the structure of Markovian KMS-states of quantum spin chains as wel l as of multidimensional quantum spin lattices.