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arXiv:1704.08420

Changes to the t-J Model From Inclusion of Two-Site Nearest-Neighbor Coulomb Interactions

Tao Sun

Published Apr 27, 2017• 0 citations
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Abstract

To date, the Hubbard model and its strong coupling limit, the t-J model, serve as the canonical model for strongly correlated electron systems in solids. Approximating the Coulomb interaction by only the on-site term (Hubbard U-term), however, may not be sufficient to describe the essential physics of interacting electron systems. We develop a more complete model in which all the next leading order terms besides the on-site term are retained. Moreover, we discuss how the inclusion of these neglected interaction terms in the Hubbard model changes the t-J model.

DOI
10.48550/arxiv.1704.08420

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To date, the Hubbard model and its strong coupling limit, the t-J model, serve as the canonical model for strongly correlated electron systems in solids. Approximating the Coulomb interaction by only the on-site term (Hubbard U-term), however, may not be sufficient to describe the essential physics of interacting electron systems. We develop a more complete model in which all the next leading order terms besides the on-site term are retained. Moreover, we discuss how the inclusion of these neglected interaction terms in the Hubbard model changes the t-J model.
To date, the Hubbard model and its strong coupling limit, the t-J model, serve as the canonical model for strongly correlated electron systems in solids. Approximating the Coulomb interaction by only the on-site term (Hubbard U-term), however, may not be sufficient to describe the essential physics of interacting electron systems. We develop a more complete model in which all the next leading order terms besides the on-site term are retained. Moreover, we discuss how the inclusion of these neglected interaction terms in the Hubbard model changes the t-J model.
Originally, the Hubbard model has been derived for describing the behaviour of strongly-correlated electrons in solids. However, since over a decade now, variations of it are also routinely being imple-mented with ultracold atoms in optical lattices, allowing their study in a clean, essentially defect-free environment. Here, we review some of the rich literature on this subject, with a focus on more recent non-standard forms of the Hubbard model. After an introduction to standard (fermionic and bosonic) Hubbard models, we discuss briefly common models for mixtures, as well as the so called extended Bose-Hubbard models, that include interactions between neighboring sites, next-neighboring sites, and so on. The main part of the review discusses the importance of additional terms appearing when refining the tight-binding approximation on the original physical Hamiltonian. Even when restricting the models to the lowest Bloch band is justified, the standard approach neglects the density-induced tunneling (which has the same origin as the usual on-site interaction). The importance of these contri-
We investigate the general applicability of the standard Peierls-Hubbard model, involving both on-site (UUU) and nearest-neighbor (VVV) Coulomb repulsions, by adding nearest-neighbor off-diagonal terms representing the bond (WWW) and mixed bond-site (XXX) electron-electron repulsive interactions. For a broad range of the site-diagonal Hubbard parameters (U,VU,VU,V), we find that the off-diagonal terms (W,XW,XW,X) initially enhance dimerization, thereby stabilizing the dimerized ground state.
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.
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.