The low-energy states and directional long-range order in the two-dimensional quantum compass model
Wen‐Long You, Guang-Shan Tian, Hai-Qing Lin · Journal of Physics A Mathematical and Theoretical · 2010
In the present paper, we study the properties of the two-dimensional quantum compass model by a mathematically rigorous approach. Based on the Perron?Fr?benius theorem and the reflection positivity method, we show that the low-energy spectrum of this model is of one-dimensional type. Furthermore, its global ground states have a directional long-range order. Our results confirm several previous conclusions obtained by either numerical or perturbation calculations