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KMS states on Z₂-crossed products of unital C^*-algebras A are characterized in terms of KMS states and graded KMS functionals of A. These functionals are shown to describe the extensions of KMS states on A to the crossed product A Z₂ and can also be characterized by the twisted center of the von Neumann algebra generated by the GNS representation corresponding to. As a particular class of examples, KMS states on Z₂-crossed products of CAR algebras with dynamics and grading given by Bogoliubov automorphisms are analysed in detail. In this case, one or two extremal KMS states are found depending on a Gibbs type condition involving the odd part of the absolute value of the Hamiltonian. As an application in mathematical physics, the extended field algebra of the Ising QFT is shown to be a Z₂-crossed product of a CAR algebra which has a unique KMS state.
Silva et al. (Fri,) studied this question.
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