Mass-imbalanced ionic Hubbard chain
Michael Sekania, D. Baeriswyl, Luka Jibuti, G. I. Japaridze · Physical review. B./Physical review. B · 2017
A repulsive Hubbard model with both spin-asymmetric hopping $({t}_{\ensuremath{\uparrow}}\ensuremath{ e}{t}_{\ensuremath{\downarrow}})$ and a staggered potential (of strength $\mathrm{\ensuremath{\Delta}})$ is studied in one dimension. The model is a compound of the mass-imbalanced $({t}_{\ensuremath{\uparrow}}\ensuremath{ e}{t}_{\ensuremath{\downarrow}},\phantom{\rule{0.16em}{0ex}}\mathrm{\ensuremath{\Delta}}=0)$ and ionic $({t}_{\ensuremath{\uparrow}}={t}_{\ensuremath{\downarrow}},\phantom{\rule{0.16em}{0ex}}\mathrm{\ensuremath{\Delta}}>0)$ 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, $U\ensuremath{\ge}0$. The amplitude of the charge modulation is largest at $U=0$, decreases with increasing $U$ and tends to zero for $U\ensuremath{\rightarrow}\ensuremath{\infty}$. The amplitude for spin alternation increases with $U$ and tends to saturation for $U\ensuremath{\rightarrow}\ensuremath{\infty}$. Charge order dominates below a value ${U}_{c}$, whereas magnetic order dominates above. The mean-field Hamiltonian has two gap parameters, ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\uparrow}}$ and ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\downarrow}}$, which have to be determined self-consistently. 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.