The Mass-Imbalanced Ionic Hubbard Chain

Abstract

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.