The Yangian symmetry of the Hubbard model

Uglov, Denis; Korepin, V. E.

doi:10.1016/0375-9601(94)90748-x

Cited by 96 publications

(103 citation statements)

References 19 publications

(15 reference statements)

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“…(2.10)). The Yangian representation (4.12) and (4.13) was first obtained by Uglov and Korepin [42,23]. It can be embedded into a larger family of Yangian representations connected with long-range-hopping extensions of the Hamiltonian (2.1) [43].…”

Section: Yangian Symmetry and Commuting Operatorsmentioning

confidence: 99%

Algebraic solution of the Hubbard model on the infinite interval

Murakami

Göhmann

1998

Nuclear Physics B

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We develop the quantum inverse scattering method for the one-dimensional Hubbard model on the infinite line at zero density. This enables us to diagonalize the Hamiltonian algebraically. The eigenstates can be classified as scattering states of particles, bound pairs of particles and bound states of pairs. We obtain the corresponding creation and annihilation operators and calculate the S-matrix. The Hamiltonian on the infinite line is invariant under the Yangian quantum group Y(su(2)). We show that the n-particle scattering states transform like n-fold tensor products of fundamental representations of Y(su(2)) and that the bound states are Yangian singlet. ‡

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Section: Yangian Symmetry and Commuting Operatorsmentioning

confidence: 99%

Algebraic solution of the Hubbard model on the infinite interval

Murakami

Göhmann

1998

Nuclear Physics B

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“…This conjecture significantly simplified the thermodynamics of the model, provided the finite set of nonlinear integral equations, and calculated very well numerically compared to the infinite set proposed by Takahashi [8]. Shortly afterwards Uglov and Korepin [15] discovered that the Hubbard Hamiltonian has the Yangians symmetry, related with the quantum groups theory, extending the already known SU(2) × SU (2) invariance of the model. As the Hubbard model has become increasingly important in condensed matter physics, it is appropriate to revisit it and provide some instructive new examples appropriate for the considered case, in order to improve the understanding of the concept.…”

Section: Introductionmentioning

confidence: 81%

On the SU(2)×SU(2) symmetry in the Hubbard model

Jakubczyk

2012

Open Physics

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Abstract:We discuss the one-dimensional Hubbard model, on finite sites spin chain, in context of the action of the direct product of two unitary groups SU(2)×SU(2). The symmetry revealed by this group is applicable in the procedure of exact diagonalization of the Hubbard Hamiltonian. This result combined with the translational symmetry, given as the basis of wavelets of the appropriate Fourier transforms, provides, besides the energy, additional conserved quantities, which are presented in the case of a half-filled, four sites spin chain. Since we are dealing with four elementary excitations, two quasiparticles called "spinons", which carry spin, and two other called "holon" and "antyholon", which carry charge, the usual spin-SU(2) algebra for spinons and the so called pseudospin-SU(2) algebra for holons and antiholons, provide four additional quantum numbers. PACS

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“…These nonlinear expressions contain quantum derivatives and, as a result, quantum groups. We note that after the super-Yangian structure in the one-dimensional Hubbard model was discovered [12], there were numerous attempts to find quantum groups in the Hubbard model, but they were unsuccessful. We use an absolutely different approach in this paper, and the discovery of quantum structures in the Hubbard model is therefore explainable.…”

Section: The Effective Functional Of the Hubbard Modelmentioning

confidence: 99%

The functional integral in the Hubbard model

Zharkov¹

2012

Theor Math Phys

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In a new functional integral approach proposed for the model, we find the regime with a deformed integration measure in which the standard integral is replaced with the Jackson integral. We indicate the relation to a p-adic functional integral. For the magnetic and electronic subsystems in the effective functional that results from the operator formulation of the Hubbard model, we find the two-parametric quantum derivative resulting in the appearance of the quantum SUrq(2) group. We establish the relation to the one-parametric quantum derivative and to the standard derivative.

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The Yangian symmetry of the Hubbard model

Cited by 96 publications

References 19 publications

Algebraic solution of the Hubbard model on the infinite interval

Algebraic solution of the Hubbard model on the infinite interval

On the SU(2)×SU(2) symmetry in the Hubbard model

The functional integral in the Hubbard model

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