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Molecular crystals and liquid crystals science technology. Section A, Molecular crystals and liquid crystals/Molecular crystals and liquid crystals science and technology. Section A, Molecular crystals and liquid crystals

Charge Gap and Interchain Correlation in Quasi-One-Dimensional Dimerized Organic Conductors

Kenji Yonemitsu

Published Apr 1, 2000• 1 citation
Publisher

Abstract

We study the relation between the charge gap and the interchain one-body correlation function in quasi-one-dimensional dimerized organic conductors at quarter filling, by applying the density matrix renormalization group method to a three-chain extended Hubbard model. The charge gap increases with the degree of dimerization in the intrachain hopping integrals. When the charge gap is larger than the interchain hopping integral, the interchain hopping correlation is strongly suppressed, as observed in the (TMTTF)2X salts.

DOI
10.1080/10587250008026196

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We study the relation between the charge gap and the interchain one-body correlation function in quasi-one-dimensional dimerized organic conductors at quarter filling, by applying the density matrix renormalization group method to a three-chain extended Hubbard model. The charge gap increases with the degree of dimerization in the intrachain hopping integrals. When the charge gap is larger than the interchain hopping integral, the interchain hopping correlation is strongly suppressed, as observed in the (TMTTF)2X salts.
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.
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.
We derive two-loop renormalization group equations for the half filled one-dimensional Hubbard chains coupled by the interchain hopping. Our renormalization group scheme for the quasi-one-dimensional electron system is a natural extension of that for the purely one-dimensional systems in the sense that transverse-momentum dependences are introduced in the ggg-ological coupling constants and we regard the transverse momentum as a patch index. We develop symmetry arguments for the particle-hole symmetric half filled Hubbard model and obtain constraints on the ggg-ological coupling constants by which resultant renormalization equations are given in a compact form. By solving the renormalization group equations numerically, we estimate the magnitude of excitation gaps and clarify that the charge gap is suppressed due to the interchain hopping but is always finite even for the relevant interchain hopping. To show the validity of the present analysis, we also apply this to the two-leg ladder system. By utilizing the field-theoretical Bosonization and Fermionization method, we derive low-energy effective theory and analyze the magnitude of all the excitation gaps in detail. It is shown that the low-energy excitations in the two-leg Hubbard ladder have $\mathrm{SO}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SO}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ symmetry when the interchain hopping exceeds the magnitude of the charge gap.
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.
We investigate the ground-state phase diagram of the quarter-filled Hubbard ladder with nearest-neighbor Coulomb repulsion VVV using the density matrix renormalization-group technique. The ground state is homogeneous at small V,V,V, a ``checkerboard'' charge-ordered insulator at large VVV and not too small on site Coulomb repulsion U, and is phase separated for moderate or large VVV and small U. The zero-temperature transition between the homogeneous and the charge-ordered phase is found to be second order. In both the homogeneous and the charge-ordered phases the existence of a spin gap mainly depends on the ratio of interchain to intrachain hopping. In the second part of the paper we construct an effective Hamiltonian for the spin degrees of freedom in the strong-coupling, charge-ordered regime that maps the system onto a frustrated spin chain. The opening of a spin gap is thus connected with spontaneous dimerization.
The magnetic susceptibility of the quarter-filled one-dimensional extended Hubbard model is calculated using the density-matrix renormalization group technique. It is found that in the charge gap regime of the model ($U> 4t $ and V>2tV > 2tV>2t), or in the metallic region with important superconductive fluctuations (U<4tU<4tU<4t and V>2tV>2tV>2t), χ(T)χ(T)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.