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arXiv:cond-mat/0412026 · Physical Review B

Dimerized phase of ionic Hubbard models

Armando A. Aligia, Cristian D. Batista

Published Mar 17, 2005• 31 citations
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Abstract

We derive an effective Hamiltonian for the ionic Hubbard model at half filling, extended to include nearest-neighbor repulsion. Using a spin-particle transformation, the effective model is mapped onto simple spin-1 models in two particular cases. Using another spin-particle transformation, a slightly modified model is mapped into an SU(3) antiferromagnetic Heisenberg model whose exact ground state is known to be spontaneously dimerized. From the effective models several properties of the dimerized phase are discussed, like ferroelectricity and fractional charge excitations. Using bosonization and recent developments in the theory of macroscopic polarization, we show that the polarization is proportional to the charge of the elementary excitations.

DOI
10.1103/physrevb.71.125110

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We derive an effective Hamiltonian for the ionic Hubbard model at half filling, extended to include nearest-neighbor repulsion. Using a spin-particle transformation, the effective model is mapped onto simple spin-1 models in two particular cases. Using another spin-particle transformation, a slightly modified model is mapped into an SU(3) antiferromagnetic Heisenberg model whose exact ground state is known to be spontaneously dimerized. From the effective models several properties of the dimerized phase are discussed, like ferroelectricity and fractional charge excitations. Using bosonization and recent developments in the theory of macroscopic polarization, we show that the polarization is proportional to the charge of the elementary excitations.
An unusual metallic phase is argued to develop in the one-dimensional ionic Hubbard model, at half-filling and zero magnetization, at intermediate electron-electron repulsion UUU when second-neighbors hopping is allowed and tuned close to a topological Lifshitz transition (connected with a change of the Fermi surface in the noninteracting system). The metallic state lies between a band insulator phase at low repulsion and a correlated (Mott-like) insulator phase at high repulsion. In approaching the latter, the model supports short-range antiferromagnetic order and spontaneous dimerization of both bond charge and nearest-neighbor antiferromagnetic correlations. A combination of mean-field and effective-field theory (bosonization) provides an analytical understanding of the physical processes underlying the argued phase transitions. The ground and low-energy excited states of finite-length chains are explored by density-matrix renormalization-group (DMRG) calculations, providing numerical evidence for the intermediate gapless phase. Such finite systems are attainable by cold atoms in optical lattices for a wide range of the parameter UUU.
We derive an effective Hamiltonian Heff{H}_{\mathrm{eff}}Heff​ for an ionic Hubbard chain, valid for $t\ensuremath{\ll}U,\ensuremath{\Delta}$, where ttt is the hopping, UUU is the Coulomb repulsion, and $\ensuremath{\Delta}$ is the charge-transfer energy. Heff{H}_{\mathrm{eff}}Heff​ is the minimal model for describing the transition between the band insulator (BI) ($\ensuremath{\Delta}\ensuremath{-}U\ensuremath{\gg}t$) and the Mott insulator (MI) ($U\ensuremath{-}\ensuremath{\Delta}\ensuremath{\gg}t$). Using spin-particle transformations [Phys. Rev. Lett. 86, 1082 (2001)], we map ${H}_{\mathrm{eff}}(U=\ensuremath{\Delta})$ into an SU(3) antiferromagnetic Heisenberg model whose exact ground state is known. In this way, we show rigorously that a spontaneously dimerized insulating ferroelectric phase appears in the transition region between the BI and the MI.
I extend to charge and bond operators the transformation that maps the ionic Hubbard model at half filling onto an effective spin Hamiltonian. Using the transformed operators I calculate the amplitude of the charge-density wave in different dimensions D. In one dimension, the charge-charge correlations at large distance d decay as ${d}^{\ensuremath{-}3}{\mathrm{ln}}^{\ensuremath{-}3/2}d,$ in spite of the finite charge gap, due to remaining charge-spin coupling. Bond-bond correlations decay as $(\ensuremath{-}{1)}^{d}{d}^{\ensuremath{-}1}{\mathrm{ln}}^{\ensuremath{-}3/2}d$ as in the usual Hubbard model.
We study the one-dimensional extended Hubbard model with alternating size of the hopping integrals using the density-matrix renormalization group method. We calculate the spin gap, the Tomonaga-Luttinger parameter, and the charge-density-wave order parameter for various dimerizations, interaction strengths, and band fillings. At half band-filling the spin and charge excitations are gapped but these gaps disappear for infinitesimal hole doping. At quarter filling, the umklapp scattering in the half-filled lower Peierls band generates a gap for the charge excitations but the gapless spin excitations can be described in terms of an effective antiferromagnetic Heisenberg model. Beyond a critical strength for the nearest-neighbor interaction, the dimerized extended Hubbard model at quarter filling develops a charge-density-wave ground state. The dimerization and the nearest-neighbor Coulomb interaction strongly reduce the Tomonaga-Luttinger parameter from its value for the bare Hubbard model. We discuss the relevance of our findings for the Bechgaard salts.