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Recently, we demonstrated rigorously the stability of charge-stripe phases in 2D quantum-particle systems that are described by extended Falicov–Kimball Hamiltonians, with the quantum hopping particles being either spinless fermions or hardcore bosons. In this paper, by means of the same methods, we show that an arbitrary small anisotropy of nearest-neighbor hopping eliminates the π/2-rotation degeneracy of dimeric and axial-stripe phases and orients them in the direction of the weaker hopping. Due to the same anisotropy the obtained phase diagrams of fermions show a tendency to become similar to those of hardcore bosons.

Charge-Stripe Phases Versus a Weak Anisotropy of Nearest-Neighbor Hopping