Effective Hamiltonian for a half-filled asymmetric ionic Hubbard chain with alternating on-site interaction

A repulsive Hubbard model with both spin-asymmetric hopping (t ↑ = t ↓ ) and a staggered potential (of strength ) is studied in one dimension. The model is a compound of the mass-imbalanced (t ↑ = t ↓ , = 0) and ionic (t ↑ = t ↓ , > 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 → ∞. The amplitude for spin alternation increases with U and tends to saturation for U → ∞. Charge order dominates below a value U c , whereas magnetic order dominates above. The mean-field Hamiltonian has two gap parameters, ↑ and ↓ , 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.

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“…of Eq. (33), which can also be written as A ↑ A ↓ /(λ + λ − ). The eigenvalue λ − decreases when U c is approached and is very small at U c .…”

Section: B Fidelity Susceptibilitymentioning

confidence: 99%

Mass-imbalanced ionic Hubbard chain

et al. 2017

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“…If only the SU (2) symmetry is explicitly broken (t ↑ = t ↓ , ∆/t ↑ = 0), an asymmetry in the spin sector appears. In fact, for the strong coupling limit, U ≫ t ↑ , t ↓ , the Hamiltonian (1) can be effectively mapped into the anisotropic XXZ Heisenberg Hamiltonian [52]:…”

Section: Introductionmentioning

confidence: 99%

“…When both symmetries, traslational and SU (2), are broken, the system is fully described at the strong coupling limit by the following effective Hamiltonian [52,54]:…”

Section: Introductionmentioning

confidence: 99%

Mass imbalance in the ionic Hubbard model: a DRMG study

Padilla-González,

Franco,

Silva-Valencia

2021

Preprint

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We investigated the ionic Hubbard model with mass imbalance in one dimension, using the density matrix renormalization group method. This model exhibits a band insulator phase and an antiferromagnetic one, both with a finite spin gap. We found that this quantum phase transition is continuous, unalike the previous mean-field theory result. The von Neumann block entropy is maximum at the critical points, a fact that we used to build the phase diagram.

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