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arXiv:cond-mat/9910133 · Journal of the Physical Society of Japan

Electronic States in Half-Filled Correlated System with Alternating Potential

Masahisa Tsuchiizu, Yoshikazu Suzumura

Published Dec 15, 1999• 13 citations
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Abstract

The effect of an alternating potential on a one-dimensional half-filled Hubbard model with repulsive interaction has been examined by applying the renormalization group method to the bosonized Hamiltonian. The electronic state, which is determined by the competition between alternating potential and umklapp scattering, is calculated where the relevance and the irrelevance of the alternating potential leads to the band insulator and the Mott insulator respectively. The excitation gaps for charge and spin fluctuations are calculated for both states.

DOI
10.1143/jpsj.68.3966

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The effect of an alternating potential on a one-dimensional half-filled Hubbard model with repulsive interaction has been examined by applying the renormalization group method to the bosonized Hamiltonian. The electronic state, which is determined by the competition between alternating potential and umklapp scattering, is calculated where the relevance and the irrelevance of the alternating potential leads to the band insulator and the Mott insulator respectively. The excitation gaps for charge and spin fluctuations are calculated for both states.
We investigate the ground-state phase diagram of the one-dimensional 'ionic' Hubbard model with an alternating periodic potential at half-filling by numerical diagonalization of finite systems with the Lanczos and density matrix renormalization group methods. We identify an insulator–insulator phase transition from a band to a correlated insulator with simultaneous charge and bond-charge order. The transition point is characterized by the vanishing of the optical excitation gap while simultaneously the charge and spin gaps remain finite and equal. Indications for a possible second transition into a Mott-insulator phase are discussed.
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A one-dimensional electron system at quarter-filling has been examined by applying the renormalization group method to a bosonized model with on-site (U) and nearest-neighbor (V) repulsive interactions. By evaluating both normal scattering and Umklapp scattering perturbatively, we obtain a phase diagram in which a metallic state with a 2k_F spin density wave (k_F is the Fermi wave number) moves into an insulating state with charge disproportionation of a 4k_F charge density wave with an increase in both U and V. The effect of the next-nearest-neighbor repulsion is also discussed.
Discrepancies between the single-particle band structure and the exact many-particle behavior are particularly striking in one-dimensional systems. The one-dimensional alternating Hubbard model is especially interesting as a nontrivial model for conjugated polymer chains, such as polyacetelyne. We study this model for chains of 60 sites using the density-matrix renormalization-group method. We obtain the first electronic and magnetic excited-state energies at half filling as a function of an alternating hopping parameter and on-site electron-electron interaction. We also study the effect of the interaction on the dimerization and discuss its relation to the charge gap and spin triplet gap. In addition, we calculate the local spin and charge densities of some excited states, which manifest a clear crossover from bandlike to strongly correlated behavior.
We have investigated the ground-state phase diagram of the one-dimensional Hubbard model with alternating chemical potentials at half-filling by bosonization technique and the Gaussian wave functional method. We calculate variations of the charge density wave (CDW) and the spin density wave (SDW) gaps, ad well as their classical trajectory c,s with increasing on-site Coulomb repoulsion potential. For the fixed potential, it is found that the transition from the band insulator (BI) to the spontaneously dimerized insulator (SDI) is of the Ising type, at which charge gap vanishes, while the transition from SDI to the Mott insulator (MI) is of the KT type.
We study the phase diagram of a one-dimensional extended Hubbard model with antiferromagnetic exchange interaction analytically and numerically. The bosonization and transfer-matrix renormalization group methods are used in the corresponding coupling regimes. At half-filling, the system is a Mott insulator with a finite spin excitation gap if the on-site Coulomb repulsion is fairly smaller than the antiferromagnetic exchange JJJ. This Mott insulator is characterized by the bond-charge-density-wave order or spontaneously dimerization. In the weak-coupling regime where the spin-charge separation holds approximately, the critical point separating the gapless and gapped spin liquid phases is ${U}_{c}\ensuremath{\sim}J∕2$. However, as JJJ increases, the spin-charge couplings become important and the critical point Uc{U}_{c}Uc​ is significantly suppressed and eventually tends to zero as $J\ensuremath{\rightarrow}\ensuremath{\infty}$. Away from half-filling, the charge gap completely collapses but the spin gap persists.