Quantum Phase Transition in the One-Dimensional XZ Model

W. Brzezicki a and A.M. Oleś a,b a M. Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, PL-30-059 Kraków, Poland b Max-Planck-Institut für Festkörperforschung , Heisenbergstrasse 1, D-70569 Stuttgart, Germany

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We introduce a one-dimensional XZ model with alternating σizσi+1z and σixσi+1x interactions on even/odd bonds, interpolating between the Ising model and the quantum compass model. We present two ways of its exact solution by: (i) mapping to the quantum Ising models, and (ii) using fermions with spin 1/2. In certain cases the nearest neighbor pseudospin correlations change discontinuously at the quantum phase transition, where one finds highly degenerate ground state of the 1D compass model.

DOI: 10.12693/APhysPolA.115.162 PACS numbers: 75.10.Jm, 03.67.-a, 05.70.Fh