Abstract
The ground state magnetic phase diagram of the one-dimensional quantum compass model (QCM) is studied using the numerical Lanczos method. A detailed numerical analysis of the low energy excitation spectrum is presented. The energy gap and the spin-spin correlation functions are calculated for finite chains. Two kind of the magnetic long-range orders, the Neel and a type of the stripe-antiferromagnet, in the ground state phase diagram are identified. Based on the numerical analysis, the first and second order quantum phase transitions in the ground state phase diagram are identified.
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