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arXiv:cond-mat/9410026 · Physical Review Letters

New Supersymmetric and Exactly Solvable Model of Correlated Electrons

Anthony J. Bracken, M. D. Gould, Jon Links, Yao-Zhong Zhang

Published Apr 3, 1995• 145 citations
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Abstract

A new lattice model is presented for correlated electrons on the unrestricted ${4}^{L}$-dimensional electronic Hilbert space ${\ensuremath{\bigotimes}}_{n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1}^{L}{\mathbf{C}}^{4}$ (where $L$ is the lattice length). It is a supersymmetric generalization of the Hubbard model, but differs from the extended Hubbard model proposed by Essler, Korepin, and Schoutens. The supersymmetry algebra of the new model is superalgebra gl(2 $|$1). The model contains one symmetry-preserving free real parameter which is the Hubbard interaction parameter $U$, and has its origin here in the one-parameter family of inequivalent typical 4-dimensional irreducible representations of gl(2 $|$1). On a one-dimensional lattice, the model is exactly solvable by the Bethe ansatz.

DOI
10.1103/physrevlett.74.2768

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By considering the one-parameter family of inequivalent typical four-dimensional irreps of U-q[gl(2 1)], we may construct the anisotropic supersymmetric U model. This is a model for correlated electrons acting on the unrestricted 4(L)-dimensional electronic Hilbert space x(n=1)(L)C(4), where L is the lattice length. An important characteristic of the model is that it contains two symmetry-preserving free real parameters. Eigenstates of the model are determined by the algebraic Bethe ansatz on a one-dimensional periodic lattice.
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