Functional equations and quantum separation of variables for 3d spin models

Sergey Sergeev

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The recently proposed invariant formulation of the auxiliary linear problem for 3d integrable models provides several new ideas for solving the spectral problem of 3d spin models, e.g., the Zamolodchikov–Bazhanov–Baxter model in its vertex formulation. This paper announces results following from the invariant formulation. We formulate the class of 3d spin models that are essentially appropriately parameterized inhomogeneous Zamolodchikov–Bazhanov–Baxter models, present an expression for the generating function of the complete set of matrices commuting with the transfer matrix of this model (integrals of motion), give the functional equations defining the eigenvalues of the integrals of motion and the transfer matrices, explicitly describe the groupoid of isospectral transformations of the initial system of integrals of motion, and finally give an explicit parameterization of a projection operator onto the separated states in the sense of the quantum separation of variables (functional Bethe ansatz)
Original languageEnglish
Pages (from-to)226-237
Number of pages12
JournalTheoretical and Mathematical Physics
Volume138
Publication statusPublished - 2004
Externally publishedYes

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Integrals of Motion
Separation of Variables
Spin Models
3D Model
Functional equation
Transfer Matrix
Formulation
Integrable Models
Invariant
Bethe Ansatz
Groupoid
Projection Operator
Spectral Problem
formulations
Parameterization
Generating Function
Model
Eigenvalue
Vertex of a graph
parameterization

Cite this

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title = "Functional equations and quantum separation of variables for 3d spin models",
abstract = "The recently proposed invariant formulation of the auxiliary linear problem for 3d integrable models provides several new ideas for solving the spectral problem of 3d spin models, e.g., the Zamolodchikov–Bazhanov–Baxter model in its vertex formulation. This paper announces results following from the invariant formulation. We formulate the class of 3d spin models that are essentially appropriately parameterized inhomogeneous Zamolodchikov–Bazhanov–Baxter models, present an expression for the generating function of the complete set of matrices commuting with the transfer matrix of this model (integrals of motion), give the functional equations defining the eigenvalues of the integrals of motion and the transfer matrices, explicitly describe the groupoid of isospectral transformations of the initial system of integrals of motion, and finally give an explicit parameterization of a projection operator onto the separated states in the sense of the quantum separation of variables (functional Bethe ansatz)",
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Functional equations and quantum separation of variables for 3d spin models. / Sergeev, Sergey.

In: Theoretical and Mathematical Physics, Vol. 138, 2004, p. 226-237.

Research output: Contribution to journalArticle

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AU - Sergeev, Sergey

PY - 2004

Y1 - 2004

N2 - The recently proposed invariant formulation of the auxiliary linear problem for 3d integrable models provides several new ideas for solving the spectral problem of 3d spin models, e.g., the Zamolodchikov–Bazhanov–Baxter model in its vertex formulation. This paper announces results following from the invariant formulation. We formulate the class of 3d spin models that are essentially appropriately parameterized inhomogeneous Zamolodchikov–Bazhanov–Baxter models, present an expression for the generating function of the complete set of matrices commuting with the transfer matrix of this model (integrals of motion), give the functional equations defining the eigenvalues of the integrals of motion and the transfer matrices, explicitly describe the groupoid of isospectral transformations of the initial system of integrals of motion, and finally give an explicit parameterization of a projection operator onto the separated states in the sense of the quantum separation of variables (functional Bethe ansatz)

AB - The recently proposed invariant formulation of the auxiliary linear problem for 3d integrable models provides several new ideas for solving the spectral problem of 3d spin models, e.g., the Zamolodchikov–Bazhanov–Baxter model in its vertex formulation. This paper announces results following from the invariant formulation. We formulate the class of 3d spin models that are essentially appropriately parameterized inhomogeneous Zamolodchikov–Bazhanov–Baxter models, present an expression for the generating function of the complete set of matrices commuting with the transfer matrix of this model (integrals of motion), give the functional equations defining the eigenvalues of the integrals of motion and the transfer matrices, explicitly describe the groupoid of isospectral transformations of the initial system of integrals of motion, and finally give an explicit parameterization of a projection operator onto the separated states in the sense of the quantum separation of variables (functional Bethe ansatz)

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EP - 237

JO - Theoretical and Mathematical Physics(Russian Federation)

JF - Theoretical and Mathematical Physics(Russian Federation)

SN - 0040-5779

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