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# The Mass-Imbalanced Ionic Hubbard Chain

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### 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.

### Most cited references54

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### Many-Body Physics with Ultracold Gases

(2007)
This article reviews recent experimental and theoretical progress on many-body phenomena in dilute, ultracold gases. Its focus are effects beyond standard weak-coupling descriptions, like the Mott-Hubbard-transition in optical lattices, strongly interacting gases in one and two dimensions or lowest Landau level physics in quasi two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near Feshbach resonances in the BCS-BEC crossover.
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### Cold bosonic atoms in optical lattices

(1998)
The dynamics of an ultracold dilute gas of bosonic atoms in an optical lattice can be described by a Bose-Hubbard model where the system parameters are controlled by laser light. We study the continuous (zero temperature) quantum phase transition from the superfluid to the Mott insulator phase induced by varying the depth of the optical potential, where the Mott insulator phase corresponds to a commensurate filling of the lattice (optical crystal''). Examples for formation of Mott structures in optical lattices with a superimposed harmonic trap, and in optical superlattices are presented.
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### Feshbach Resonances in Ultracold Gases

(2008)
Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This Review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules.
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### Author and article information

###### Journal
2017-04-24
1704.07459