Yang-Baxter equation and reflection equations in integrable models

“…We construct T m (u) as the supertrace of a monodromy matrix built of the elementary R-matrix blocks [24]. We introduce the N spaces V ℓ i and N operators R m, ℓ i (u):…”

Section: Homogeneous Periodic Chain 41 Commuting Transfer Matricesmentioning

confidence: 99%

Heisenberg spin chains based on sℓ(2|1) symmetry

Derkachov¹,

Karakhanyan²,

Kirschner³

2000

Nuclear Physics B

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“…where the parameter ν m characterizes the impurity strength at site m. Now we suppose that the supermatrices K ± are the solutions of the graded RE [25,26],…”

Section: Integrable Impurities In the Bulkmentioning

confidence: 99%

Integrable impurities for an open fermion chain

Guan

Grimm

Römer

et al. 2000

J. Phys. A: Math. Gen.

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Abstract. Employing the graded versions of the Yang-Baxter equation and the reflection equations, we construct two kinds of integrable impurities for a small-polaron model with general open boundary conditions: (a) we shift the spectral parameter of the local Lax operator at arbitrary sites in the bulk, and (b) we embed the impurity fermion vertex at each boundary of the chain. The Hamiltonians with different types of impurity terms are given explicitly. The Bethe ansatz equations, as well as the eigenvalues of the Hamiltonians, are constructed by means of the quantum inverse scattering method. In addition, we discuss the ground-state properties in the thermodynamic limit.

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“…Solutions of the Yang-Baxter equation, in particular ones with sℓ(2) or sℓ(2|1) symmetry, are used in constructing a number of statistical models [1,2,3,4,5,6,8,26] and are applied in analyzing the high-energy Regge [16,17,18,22] and Bjorken asymptotics [19,20,21] of four -dimensional gauge theories.…”

Section: Introductionmentioning

confidence: 99%

Universal -matrix as integral operator

2001

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Abstract.We derive the integral operator form for the general rational solution of the Yang-Baxter equation with sℓ(2|1) symmetry. Considering the defining relations for the kernel of the Roperator as a system of second order differential equations we observe remarkable reduction to a system of simple first order equations. The obtained kernel of R-operator has a very simple structure. To illustrate all this in the simplest situation we treat also the sℓ(2) case.

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Yang-Baxter equation and reflection equations in integrable models

Cited by 45 publications

References 54 publications

Heisenberg spin chains based on sℓ(2|1) symmetry

Heisenberg spin chains based on sℓ(2|1) symmetry

Integrable impurities for an open fermion chain

Universal -matrix as integral operator

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