Quantum Phase Transition in the One-Dimensional XZ Model

We introduce a one-dimensional (1D) XZ model with alternating ${\sigma }_i^z{\sigma }_{i+1}^z$ and ${\sigma }_i^x{\sigma }_{i+1}^x$ 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.