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Some ground-state expectation values for the free parafermion \(Z(N)\) spin chain. (English) Zbl 1459.82013

Summary: We consider the calculation of ground-state expectation values for the non-Hermitian \(Z(N)\) spin chain described by free parafermions. For \(N = 2\) the model reduces to the quantum Ising chain in a transverse field with open boundary conditions. Use is made of the Hellmann-Feynman theorem to obtain exact results for particular single site and nearest-neighbor ground-state expectation values for general \(N\) which are valid for sites deep inside the chain. These results are tested numerically for \(N = 3\), including how they change as a function of distance from the boundary.

MSC:

82B10 Quantum equilibrium statistical mechanics (general)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics

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