A repulsive Hubbard model with both spin-asymmetric hopping (${ t_\uparrow\neq t_\downarrow}$) and a staggered potential (of strength $\Delta$) is studied in one dimension. The model is a compound of the mass-imbalanced (${ t_\uparrow\neq t_\downarrow}$, ${ \Delta=0}$) and ionic (${ t_\uparrow = t_\downarrow}$, ${ \Delta>0}$) 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, ${ U\geqslant 0}$. The amplitude of the charge modulation is largest at ${ U=0}$, decreases with increasing $U$ and tends to zero for ${ U\rightarrow\infty}$. The amplitude for spin alternation increases with $U$ and tends to saturation for ${ U\rightarrow\infty}$. Charge order dominates below a critical value $U_c$, whereas magnetic order dominates above. The mean-field Hamiltonian has two gap parameters, $\Delta_\uparrow$ and $\Delta_\downarrow$, 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.
Categories: cond-mat.str-el