Mass-Imbalanced Ionic Hubbard Chain

Abstract

A repulsive Hubbard model with both spin-asymmetric hopping ($t_{\uparrow }\ne t_{\downarrow }$) and a staggered potential (of strength $\Delta$) is studied in one dimension. The model is a compound of the mass-imbalanced ($t_{\uparrow }\ne t_{\downarrow }$, $\Delta =0$) 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, $U⩾0$. The amplitude of the charge modulation is largest at $U=0$, decreases with increasing $U$ and tends to zero for $U\to \infty$. The amplitude for spin alternation increases with $U$ and tends to saturation for $U\to \infty$. 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.

14 pages, 8 figures

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