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Journal of the Physical Society of Japan

Dimensionality Effects on the Charge Gap in the Dimerized Hubbard Model at Quarter Filling: the Density-Matrix and Perturbative Renormalization-Group Approaches

Kenji Yonemitsu, Jun‐ichiro Kishine

Published Jul 15, 2000• 3 citations
Publisher

Abstract

We study dimensionality effects on the charge gap in the dimerized Hubbard model at quarter filling, with two approaches. First, we examine three chains coupled via the interchain one-particle hopping integral t b , by the density-matrix renormalization-group (DMRG) method. Next, we consider the d =1+ε dimensional model, using the perturbative renormalization-group (PRG) method. The dimensionality is controlled through t b and ε, respectively. Both approaches lead to the conclusion that, for a finite dimerization ratio, the charge gap decreases as the dimensionality increases.

DOI
10.1143/jpsj.69.2107

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The spin gap of a one-dimensional repulsive Hubbard model is numerically calculated with the density-matrix renormalization group, with a special emphasis on the effect of a next-nearest-neighbor hopping ${(t}^{\ensuremath{'}})$ and the nearest-neighbor ferromagnetic exchange (J)(J)(J) interaction. At half filling, a significant spin gap opens if $|{t}^{\ensuremath{'}}|\ensuremath{\simeq}|t|$ and J=0J=0J=0, in agreement with the weak-coupling theory, while the gap is strongly suppressed by the introduction of JJJ. On the other hand, the quarter-filled system has very small spin gaps regardless of the values of ${t}^{\ensuremath{'}}$ and JJJ. Implications for the CuO2{\mathrm{CuO}}_{2}CuO2​ chain in Sr14Cu24O41{\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}Sr14​Cu24​O41​ and related materials are discussed.
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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.