A repulsive Hubbard model with both spin-asymmetric hopping (t ↑ = t ↓ ) and a staggered potential (of strength ) is studied in one dimension. The model is a compound of the mass-imbalanced (t ↑ = t ↓ , = 0) and ionic (t ↑ = t ↓ , > 0) Hubbard models, and may be realized by cold atoms in engineered optical lattices. We use mostly mean-field theory to determine the phases and phase transitions in the ground state for a half-filled band (one particle per site). We find that a period-two modulation of the particle (or charge) density and an alternating spin density coexist for arbitrary Hubbard interaction strength, U 0. The amplitude of the charge modulation is largest at U = 0, decreases with increasing U and tends to zero for U → ∞. The amplitude for spin alternation increases with U and tends to saturation for U → ∞. Charge order dominates below a value U c , whereas magnetic order dominates above. The mean-field Hamiltonian has two gap parameters, ↑ and ↓ , which have to be determined self-consistently. For U < U c both parameters are positive, for U > U c they have different signs, and for U = U c one gap parameter jumps from a positive to a negative value. The weakly first-order phase transition at U c can be interpreted in terms of an avoided criticality (or metallicity). The system is reluctant to restore a symmetry that has been broken explicitly.
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