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arXiv:cond-mat/9605117 · Physical review. B, Condensed matter

Intersite Coulomb interaction and Heisenberg exchange

R. Eder, Jeroen van den Brink, G. A. Sawatzky

Published Jul 1, 1996• 14 citations
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Abstract

Based on exact diagonalization results for small clusters we discuss the effect of intersite Coulomb repulsion in Mott-Hubbard or charge transfers insulators. Whereas the exchange constant $J$ for direct exchange is enhanced by intersite Coulomb interaction, that for superexchange is suppressed. The enhancement of $J$ in the single-band models holds up to the critical value for the charge density wave (CDW) instability, thus opening the way for large values of $J$. Single-band Hubbard models with sufficiently strong intersite repulsion to be near a CDW instability thus may provide physical realizations of $t\ensuremath{-}J$-like models with the "unphysical" parameter ratio $\frac{J}{t}\ensuremath{\approx}1$.

DOI
10.1103/physrevb.54.r732

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We consider the influence of a nearest-neighbor Coulomb interaction in an extended Hubbard model and introduce an interaction term which simulates atomic polarizabilities. The inclusion of atomic polarizabilities in the model has the effect of screening the on-site Coulomb interaction for charged excitations, unlike a neighbor Coulomb interaction which reduces energies of neutral local excitations, leaving the conductivity gap unchanged. This is supported by an exact diagonalization study on small, mainly one-dimensional, extended Mott-Hubbard systems. For large V, the system undergoes a phase transition from a spin-density wave (SDW) to a charge-density wave (CDW). It is shown that the SDW/CDW phase transition cannot be described correctly when using effective parameters, but that screening effects have to be included explicitly. Also other phases, one of which is ferroelectric, appear when atomic polarizabilities are included in the model Hamiltonian. We study C60{\mathrm{C}}_{60}C60​ in terms of the degenerate extended Hubbard model with screening effects.
In the first part of the paper, we study the stability of antiferromagnetic (AF), charge density wave (CDW), and superconducting (SC) states within the t-J-U-V model of strongly correlated electrons by using the statistically consistent Gutzwiller approximation (SGA). We concentrate on the role of the intersite Coulomb interaction term V in stabilizing the CDW phase. In particular, we show that the charge ordering appears only above a critical value of V in a limited hole-doping range δ. The effect of the V term on SC and AF phases is that a strong interaction suppresses SC, whereas the AF order is not significantly influenced by its presence. In the second part, separate calculations for the case of a pure SC phase have been carried out within an extended approach (the diagrammatic expansion for the Gutzwiller wave function, DE-GWF) in order to analyze the influence of the intersite Coulomb repulsion on the SC phase with the higher-order corrections included beyond the SGA method. The upper concentration for the SC disappearance decreases with increasing V, bringing the results closer to experiment. In appendices A and B we discuss the ambiguity connected with the choice of the Gutzwiller renormalization factors within the renormalized mean filed theory when either AF or CDW orders are considered. At the end, we overview briefly the possible extensions of the current models to put descriptions of the SC, AF, and CDW states on equal footing.
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An extended Hubbard model that includes not only on-site but also intersite Coulomb repulsion and distant transfer is numerically investigated using the exact Lanczos diagonalization method for finite-size systems up to L=20L=20L=20 sites. The aim is to study the charge order and unconditional dimerization of a chain at density $\ensuremath{\rho}=0.4$. From the analysis of the spin and charge correlation functions, we deduce the formation of a dimer insulating state which is a Wigner lattice-type charge ordered state. The next-nearest-neighbor hopping t2{t}_{2}t2​ enhances the intradimer correlations and weakens the interdimer correlations. Implications for the CuO2\mathrm{Cu}{\mathrm{O}}_{2}CuO2​ chains in Sr14Cu24O41{\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}Sr14​Cu24​O41​ are discussed.
To the conventional Peierls-Hubbard model, involving both on-site (U) and nearest-neighbor (V) Coulomb repulsions, we add ``off-diagonal'' terms, not expressible purely in terms of site densities, representing bond-bond (W) and mixed bond-site (X) electron-electron repulsive interactions involving nearest neighbors. We review earlier analyses of these interactions and discuss relative magnitudes of the parameters in applications to real materials. As a specific illustration, we investigate the effects of the off-diagonal W and X terms on dimerization in the one-dimensional, half-filled-band Peierls-Hubbard models, which have been widely applied to conjugated polymers (such as trans-polyacetylene) and to related quasi-one-dimensional charge-density wave (CDW) systems. Using both weak- and strong-coupling perturbation theory for large systems and exact diagonalizations of small systems, we investigate thoroughly the nature of the ground state of the model. For a broad range of the site-diagonal Hubbard parameters (U,V), including the values believed to be relevant to trans-polyacetylene, we find that the off-diagonal terms (W,X) initially enhance dimerization, thereby stabilizing the dimerized [or bond-order-wave (BOW)] ground state. For (unphysically) large values of W relative to U and V, dimerization is destroyed, and the BOW ground state goes over to a ferromagnetic ground state or a CDW ground state, depending on the relative sizes of U, V, and W. We conclude with a general discussion of the applicability of the Peierls-Hubbard models to quasi-one-dimensional materials, including the potential importance of the breaking of charge conjugation (``particle-hole'') symmetry by the X term.
Strong correlations effects, which are often associated to the approach to a Mott insulating state, in some cases may be observed even far from half filling. This typically happens whenever the intersite Coulomb repulsion induces a tendency toward charge ordering, an effect that confines the electrons, and in turn favors local moment formation, i.e., Mott localization. A distinct intermediate regime then emerges as a precursor of such a Wigner-Mott transition, which is characterized by both charge and spin correlations, displaying large mass enhancements and strong renormalizations of other Fermi-liquid parameters. Here we present a careful study of a quarter-filled extended Hubbard model---a simple example where such physics can be studied in detail, and discuss its relevance for the understanding of the phenomenology of low-density two-dimensional electron gases.