An Exact Approach to the Diluted Hubbard Model
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AN EXACT APPROACH TO THE DILUTED HUBBARD MODEL CHUMIN WANG, 0. NAVARRO, and R. OVIEDO-ROA Instituto de Investigaciones en Materiales, U.N.A.M. Apartado Postal 70-360, 04510, Mexico D.F., MEXICO
ABSTRACT A new method to solve the extended Hubbard Hamiltonian for systems with few electrons is reported. This method is based on mapping the original many-body problem onto a tight-binding one in a higher dimensional space, which can be solved exactly. For oneand two-dimensional periodic lattices, the real-space pairing problem of two electrons with parallel and anti-parallel spins is analyzed by looking at the binding energy, the coherence length and the mobility of electron pairs. Likewise, some results of the three-body correlation are also reported. INTRODUCTION Recently, there has been an upsurge of interest in strongly-correlated Fermi systems, mainly triggered by the discovery of the new high-T. copper oxide superconductors [1]. In particular, the real-space electronic correlation in low-dimensional systems has been extensively studied by using the Hubbard model [2]. This model has the advantage of being simple and general, because does not depend explicitly on the nature of interactions between electrons. The single-band extended Hubbard Hamiltonian is given by
H= E t ,a
+V nE, nij++2 E njn 1,
(1)
i
where the hopping parameter tij = -1 for i and j nearest neighbors, U is the strength of the on-site interaction between electrons with opposite spins, and V is the nearest-neighbor the creation (ci,,) is wee c (,t~ + , , where steceto interaction. In Eq. (1), ni = ni~ + ni , ni, :,.: ctc~ (annihilation) operator for spin a =1 or T at site i. Despite the relevance and simplicity of the Hubbard model, rigorous results are obtained only for one [3] and infinite [4] dimensions. Recently, the Hubbard model has been widely studied by using different approximations. The mean-field approximation (MFA) [5] reduces the many-body problem to a one-body problem in an effective medium. However, it is well known that the MFA is not sufficient to describe electronic correlations, because the fluctuations are not included within this approximation. Another technique is the slave-boson formalism introduced by Kotliar and Ruckenstein [6]. Since in this formalism the original Hilbert space of fermion states is replaced by an enlarged Hilbert space of fermion and boson states, approximations are still necessary [7], of which the most common is the mean-field approximation. The quantum Monte Carlo simulations [8] provide a natural framework for numerical calculations in strongly interacting electron models such as the Hubbard case, but these simulations have been used only for small clusters. On the other hand, the renormalization group method [9] has been used for very large systems. This method consists in constructing iteratively a variational ground state by dividing the system into many cells. Since for each step only the lowest-lying energy states in each cell are taken into account, some times Mat. Res. Soc. Symp. Proc. Vol. 2
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