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Journal of Physics A Mathematical and General

Temperley - Lieb algebra and a new integrable electronic model

Jon Links

Published Feb 21, 1996• 6 citations
Publisher

Abstract

A new correlated electron model is presented which is derived using the quantum inverse scattering method and is thus integrable in one dimension on a periodic lattice. The R-matrix is constructed from a representation of the Temperley - Lieb algebra. The associated Hamiltonian describes correlated hopping, electron pair hopping and a generalized spin interaction.

DOI
10.1088/0305-4470/29/4/002

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A new correlated electron model is presented which is derived using the quantum inverse scattering method and is thus integrable in one dimension on a periodic lattice. The R-matrix is constructed from a representation of the Temperley - Lieb algebra. The associated Hamiltonian describes correlated hopping, electron pair hopping and a generalized spin interaction.
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New integrable variant of the one-dimensional Hubbard model with variable-range correlated hopping is studied. The Hamiltonian is constructed by applying the quantum inverse scattering method on the infinite interval at zero density to the one-parameter deformation of the L-matrix of the Hubbard model. By construction, this model has Y(su(2))\\PhiY(su(2)) symmetry in the infinite chain limit. Multiparticle eigenstates of the model are investigated through this method. z E-mail:murakami@appi.t.u-tokyo.ac.jp 2 1 Introduction As a model of strongly correlated electrons, the Hubbard model has been attracting much interest in solid state physics. Especially, in one dimension, the model is exactly solvable [1] and its thermodynamic properties can be calculated out, which give a good testing ground for theories of strongly correlated electron systems. From the point of view of the integrability of the one-dimensional Hubbard model, there have been many works, including the pioneering work o...
Abstract. A new integrable model which is a variant of the one-dimensional Hubbard model is proposed. The integrability of the model is verified by presenting the associated quantum R-matrix which satisfies the Yang-Baxter equation. We argue that the new model possesses the SO(4) algebra symmetry, which contains a representation of the η-pairing SU(2) algebra and a spin SU(2) algebra. Additionally, the algebraic Bethe ansatz is studied by means of the quantum inverse scattering method. The spectrum of the Hamiltonian, eigenvectors, as well as the Bethe ansatz equations, are discussed. PACS numbers: 71.10.Fd, 71.10.Pm. Submitted to: J. Phys. A: Math. Gen. Integrable variant of the one-dimensional Hubbard model 2
Abstract The quantum inverse scattering method is a scheme for solving integrable models in 1 + 1 dimensions, building on an R-matrix that satisfies the Yang–Baxter equation (YBE) and in terms of which one constructs a commuting family of transfer matrices. In the standard formulation, this R-matrix acts on a tensor product of vector spaces. Here, we relax this tensorial property and develop a framework for describing and analysing integrable models based on planar algebras, allowing non-separable R-operators satisfying generalised YBEs. We also re-evaluate the notion of integrals of motion and characterise when an (algebraic) transfer operator is polynomial in a single integral of motion. We refer to such models as polynomially integrable. In an eight-vertex model, we demonstrate that the corresponding transfer operator is polynomial in the natural Hamiltonian. In the Temperley–Lieb loop model with loop fugacity β ∈ C , we likewise find that, for all but finitely many β-values, the transfer operator is polynomial in the usual Hamiltonian element of the Temperley–Lieb algebra T L n ( β ) , at least for n ⩽ 17 . Moreover, we find that this model admits a second canonical Hamiltonian, and that this Hamiltonian also acts as a polynomial integrability generator for small n and all but finitely many β-values.