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We consider the calculation of ground-state expectation values for thenon-Hermitian Z(N) spin chain described by free parafermions. For N=2 the modelreduces to the quantum Ising chain in a transverse field with open boundaryconditions. Use is made of the Hellmann-Feynman theorem to obtain exact resultsfor particular single site and nearest-neighbour ground-state expectationvalues for general N which are valid for sites deep inside the chain. Theseresults are tested numerically for N=3, along with how they change as afunction of distance from the boundary.

Some ground-state expectation values for the free parafermion Z(N) spin chain