# Mass-Imbalanced Ionic Hubbard Chain

## TL;DR

This paper studies a one-dimensional mass-imbalanced ionic Hubbard model, revealing how charge and spin orderings evolve with interaction strength and identifying a weakly first-order phase transition.

## Contribution

It introduces a mean-field analysis of a combined mass-imbalanced and ionic Hubbard model, detailing phase transitions and order parameters in the ground state.

## Key findings

- Charge order dominates at low U
- Magnetic order dominates at high U
- Phase transition at critical U_c

## 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.