Two-dimensional quantum compass model in a staggered field: some rigorous results

We study the properties of the two-dimensional quantum compass model in a staggered field. Using the Perron–Fröbenius theorem and the reflection positivity method, we rigorously determine the low energy spectrum of this model and its global ground state \varPsi_0. Furthermore, we show that \varPsi_0 has a directional long-range order.