Quantum phase transition in the one-dimensional compass model using the pseudospin approach

Abstract

In the present paper, we investigate quantum phase transition in the one-dimensional compass model introduced by Brzezicki et al. [Phys. Rev. B 75, 134415 (2007)]. Unlike the previous approach based on the Jordan-Wigner transformation, we use directly the standard pseudospin representation in our investigation. Therefore, our method can be potentially applied to study rigorously the properties of the same model in higher dimensions. By applying the reflection positivity technique, we are able to determine degeneracy of the global ground state and the quantum phase-transition point of this model. We find also that the transition is of the first order. These results are consistent with the previous conclusions. However, some differences are also uncovered.