Abstract
The variational cluster approximation is used to study the ground state of the spin-asymmetric Hubbard model at half filling with geometrical frustration defined on the square lattice. We show that the three phases with N\'eel, collinear, and disorder states appear in the parameter space and we determine the orders of the phase transitions between the three phases. We corroborate quantitatively that the asymmetry due to the spin-dependent hopping parameters, which gives rise to the Ising anisotropy in spin space, suppresses the quantum fluctuations of the system and destabilizes its disordered spin state induced by the geometrical frustration.
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