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New integrable extension of the Hubbard chain with variable range hopping

Murakami, S, 村上修一, Shuichi Murakami

Published Jan 1, 1998• 3 citations
OpenAlex

Abstract

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...

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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...
We develop the quantum inverse scattering method for the one-dimensional Hubbard model on the infinite interval at zero density. R-matrix and monodromy matrix are obtained as limits from their known counterparts on the finite interval. The R-matrix greatly simplifies in the considered limit. The new R-matrix contains a submatrix which turns into the rational R-matrix of the XXX-chain by an appropriate reparametrization. The corresponding submatrix of the monodromy matrix thus provides a representation of the Y(su(2)) Yangian. From its quantum determinant we obtain an infinite series of mutually commuting Yangian invariant operators which includes the Hamiltonian. Keywords Hubbard model, quantum inverse scattering, Yangian z E-mail:murakami@appi.t.u-tokyo.ac.jp x E-mail:frank@monet.phys.s.u-tokyo.ac.jp -- Address from Oct. 1996: Physikalisches Institut der Universitat Bayreuth, TP1, 95440 Bayreuth, Germany. 1 Introduction Among the exactly solvable 1d quantum systems the Hubbard...
Integrability of strongly correlated electron systems on open chains XIANG-YU GEIn recent years, there has been a strong increase of interest in models of strongly correlated electron systems in condensed matter physics, in particular in integrable onedimensional models.Examples of such models are the one-dimensional Hubbard model, the supersymmetric t-J model, the Hubbard-like model (Bariev's chain), the so-called extended Hubbard model (EKS model), the supersymmetric U model and the eight-state supersymmetric U model.The study of integrable open-boundary conditions for strongly correlated electron models is very important for physical applications, especially for gaining insights into the behaviour of more realistic systems.The important ingredient in Sklyanin's boundary quantum inverse scattering method (QISM), which has played a key role in recent advances in the study of lattice models with open-boundaries, is a new algebraic structure, the reflection equation algebra.In this thesis, a general graded reflection equation algebra is proposed and the corresponding graded (supersymmetry) boundary QISM is formulated.The formalism is applicable to all boundary lattice systems where an invertible i?-matrix exists.As applications, some important integrable boundary conditions for various strongly correlated electron models with quantum superalgebra symmetries are constructed, including:1. Presentation of integrable open-boundary conditions for the one-dimensional qdeformed supersymmetric Essler-Korepin-Schoutens (EKS) extended Hubbard model.Determination of three different diagonal boundary if-matrices and of nine classes of integrable open-boundary conditions.Construction of the exactly solvable Hamiltonian with open-boundary terms for quantum superalgebra U q (gl(2\2)) symmetry; 2. Establishment of the quantum integrability of open-boundary conditions for the one-dimensional ^-deformed supersymmetric U model with quantum superalgebra U q (gl(2\l)} symmetry.Determination of diagonal boundary if-matrices and of integrable open-boundary conditions.Solution of the boundary system by means of the coordinate space Bethe ansatz technique, and derivation of the Bethe ansatz equations;
One dimensional exactly solvable models of strongly correlated electrons of 1/r21/r^21/r2 hopping and exchange