Abstract
The one-dimensional quantum compass model (1D-QCM) in an out-plane magnetic field is investigated by numerical and analytical methods. The presence of the 1D-QCM in an area of the ground-state magnetic phase diagram where the odd couplings are antiferromagnetic and larger than the even couplings is studied. Using pseudo spin ladder operators indicates that the 1D-QCM in an out-plane magnetic field can be mapped to the one-dimensional Ising model in a transverse magnetic field (ITF). Analytical investigation of the effective ITF Hamiltonian predicts the occurrence of two quantum phase transitions with increasing magnetic field. Also, the critical fields are obtained from this method, which are completely in agreement with the results of the numerical experiment based on the Lanczos method. This numerical method accurately determined the behavior of the energy gap, magnetization and string order parameter, and therefore it is a very useful method for indicating the ground-state phases of the system.
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