Quantum Phase Transition in the One-Dimensional XZ Model

We introduce a one-dimensional (1D) XZ model with alternating σ i σ z i+1 and σ x i σ x i+1 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.