Quantum phase transition in the one-dimensional compass model

We introduce a one-dimensional model which interpolates between the Ising model and the quantum compass model with frustrated pseudospin interactions σᵢᶻσᵢ₊₁ᶻ and σᵢˣσᵢ₊₁ˣ, alternating between even and/or odd bonds, and present its exact solution by mapping to quantum Ising models. We show that the nearest-neighbor pseudospin correlations change discontinuously and indicate divergent correlation length at the first-order quantum phase transition. At this transition, one finds the disordered ground state of the compass model with high degeneracy 2×2N∕2 in the limit of N→∞.