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Acta Physica Polonica A

An Extended Supersymmetric t-J Model

Yao-Zhong Zhang

Published Dec 1, 1995• 0 citations
Publisher

Abstract

A new lattice model is presented for correlated electrons oii the unrestricted 4 L -dimensional electronic Hilbert space ®Ln=1C4 (where L is the lattice length).It is an extension of the supersymmetric t-J model.The new model has gl(2|1) supersymmetry and contains one symmetry-preserving free real parameter α which has its origin in the one-parameter family of inequivalent typical 4-dimensionał irreps of gl(21).When α = 0, the model reduces to the supersymmetric t-J model.

DOI
10.12693/aphyspola.88.1119

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A new lattice model is presented for correlated electrons oii the unrestricted 4 L -dimensional electronic Hilbert space ®Ln=1C4 (where L is the lattice length).It is an extension of the supersymmetric t-J model.The new model has gl(2|1) supersymmetry and contains one symmetry-preserving free real parameter α which has its origin in the one-parameter family of inequivalent typical 4-dimensionał irreps of gl(21).When α = 0, the model reduces to the supersymmetric t-J model.
A new lattice model is presented for correlated electrons on the unrestricted 4L{4}^{L}4L-dimensional electronic Hilbert space ${\ensuremath{\bigotimes}}_{n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1}^{L}{\mathbf{C}}^{4}$ (where LLL 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 UUU, 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.
We present an algebraic Bethe ansatz for the supersymmetric U model for correlated electrons on the unrestricted 4L{4}^{\mathit{L}}4L-dimensional electronic Hilbert space ${\ensuremath{\bigotimes}}_{\mathit{L}}^{\mathit{n}=1}$C4{\mathit{C}}^{4}C4 (where L is the lattice length). The supersymmetry algebra of the model is the Lie superalgebra gl(2|1) and contains one symmetry-preserving free real parameter which is the Hubbard interaction parameter U. The parameter U arises from the one-parameter family of inequivalent typical four-dimensional irreps of gl(2|1). Eigenstates of the model are determined by the algebraic Bethe ansatz on a one-dimensional periodic lattice. \textcopyright{} 1996 The American Physical Society.
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.
We present an algebraic Bethe ansatz for the anisotropic supersymmetric U model for correlated electrons on the unrestricted -dimensional electronic Hilbert space (where L is the lattice length). The supersymmetry algebra of the local Hamiltonian is the quantum superalgebra and the model contains two symmetry-preserving free real parameters; the quantization parameter q and the Hubbard interaction parameter U. The parameter U arises from the one-parameter family of inequivalent typical four-dimensional irreps of . Eigenstates of the model are determined by the algebraic Bethe ansatz on a one-dimensional periodic lattice.
An integrable eight-state supersymmetric UUU model is proposed, which is a fermion model with correlated single-particle and pair hoppings as well as uncorrelated triple-particle hopping. It has a gl(3∣1)gl(3|1)gl(3∣1) supersymmetry and contains one symmetry-preserving free parameter. The model is solved and the Bethe ansatz equations are obtained.