Journal of the Physical Society of Japan

Charge Gap of the Quasi-One-Dimensional Organic Conductors: A Density-Matrix Renormalization-Group Study

Satoshi Nishimoto, Masahiro O. Takahashi, Y. Ohta

Published Jun 15, 2000• 29 citations

Abstract

The Density-matrix renormalization-group (DMRG) technique is used to study the one-dimensional (1D) dimerized Hubbard model at quarter filling. We carry out a precise calculation of the charge gap as a function of the interaction and dimerization strengths and evaluate the interaction strength of the effective 1D Hubbard model at half filling. We also examine the effect of nearest-neighbor repulsion on the charge gap, whereby we evaluate the realistic repulsive strengths for quasi-1D organic compounds.

DOI: 10.1143/jpsj.69.1594

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Journal of the Physical Society of Japan

Charge Gap of the Quasi-One-Dimensional Organic Conductors: A Density-Matrix Renormalization-Group Study

Satoshi Nishimoto, Masahiro O. Takahashi, Y. Ohta

Published Jun 15, 2000• 29 citations

Publisher

Abstract

DOI: 10.1143/jpsj.69.1594

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(J)

interaction. At half filling, a significant spin gap opens if $|{t}^{\ensuremath{'}}|\ensuremath{\simeq}|t|$ and

J=0

, in agreement with the weak-coupling theory, while the gap is strongly suppressed by the introduction of

J

. On the other hand, the quarter-filled system has very small spin gaps regardless of the values of ${t}^{\ensuremath{'}}$ and

J

. Implications for the

{\mathrm{CuO}}_{2}

chain in

{\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}

and related materials are discussed.

V > 2t

), or in the metallic region with important superconductive fluctuations (

U<4t

and

V>2t

χ(T)

displays a singularity at T=0 and an inflection point at low temperatures that are similar to what occurs in the spin-half quantum spin chain. These results, whose accuracy outdoes that of any other available technique, are useful data which allow a comparison between theory and experiment in the normal phase of the organic conductors.

1/r

hopping and the two-dimensional model with isotropic nearest-neighbor hopping. By comparing with the exact solutions for both one-dimensional models and with exact diagonalization in two dimensions, we first investigate the convergence of the ground-state energy. We find variational convergence of the energy with the number of states kept for all models and parameter sets. In contrast to the real-space algorithm, the accuracy becomes rapidly worse with increasing interaction and is not significantly better at half filling. We compare the results for different dispersion relations at fixed interaction strength over bandwidth and find that extending the range of the hopping in one dimension has little effect, but that changing the dimensionality from one to two leads to lower accuracy at weak-to-moderate interaction strength. In the one-dimensional models at half filling, we also investigate the behavior of the single-particle gap, the dispersion of spinon excitations, and the momentum distribution function. For the single-particle gap, we find that proper extrapolation in the number of states kept is important. For the spinon dispersion, we find that good agreement with the exact forms can be achieved at weak coupling if the large momentum-dependent finite-size effects are taken into account for nearest-neighbor hopping. For the momentum distribution, we compare with various weak-coupling and strong-coupling approximations and discuss the importance of finite-size effects as well as the accuracy of the DMRG.