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Quantum Phase Transition in the One-Dimensional Extended Quantum Compass Model in a Transverse Field

Quantum phase transitions in the one-dimensional extended quantum compass model in transverse field are studied by using the Jordan-Wigner transformation. This model is always gapful except at the critical surfaces where the energy gap disappears. We obtain the analytic expressions of all critical fields which drive quantum phase transitions. This model shows a rich phase diagram which includes spin-flop, strip antiferromagnetic and saturate ferromagnetic phases in addition to the phase with anti parallel ordering of spin $y$ component on odd bonds. However we study the universality and scaling properties of the transverse susceptibility and nearest-neighbor correlation functions derivatives in different regions to confirm the results obtained using the energy gap analysis.