scholarly journals Parameter-dependent solutions of the classical Yang-Baxter equation on {${\rm sl}(n,{\bf C})$}

1996 ◽  
Vol 3 (5) ◽  
pp. 517-520
Author(s):  
M. Cahen ◽  
V. De Smedt
Keyword(s):  
Baxter Equation ◽  
Parameter Dependent

Gaussian (N, z)-generalized Yang-Baxter operators

2016 ◽  
pp. 105-114
Author(s):  
Eric Rowell
Keyword(s):  
Bell States ◽  
Entangled States ◽  
Unitary Matrix ◽  
Baxter Equation ◽  
Careful Study ◽  
Standard Measurement ◽  
Measurement Basis ◽  
Parameter Dependent

We find unitary matrix solutions R˜(a) to the (multiplicative parameter-dependent) (N, z)-generalized Yang-Baxter equation that carry the standard measurement basis to m-level N-partite entangled states that generalize the 2-level bipartite entangled Bell states. This is achieved by a careful study of solutions to the Yang-Baxter equation discovered by Fateev and Zamolodchikov in 1982.

scholarly journals ON TYPE I QUANTUM AFFINE SUPERALGEBRAS

1995 ◽  
Vol 10 (23) ◽  
pp. 3259-3281 ◽  
Author(s):  
GUSTAV W. DELIUS ◽  
MARK D. GOULD ◽  
JON R. LINKS ◽  
YAO-ZHONG ZHANG
Keyword(s):  
Spectral Parameter ◽  
Lie Superalgebras ◽  
Baxter Equation ◽  
Type I ◽  
Free Fermion ◽  
General Technique ◽  
Finite Dimensional ◽  
Quantum Deformations ◽  
Free Fermion Model ◽  
Parameter Dependent

The type I simple Lie superalgebras are sl(m|n) and osp(2|2n). We study the quantum deformations of their untwisted affine extensions Uq[sl(m|n)(1)] and Uq[osp(2|2n)(1)]. We identify additional relations between the simple generators (“extra q Serre relations”) which need to be imposed in order to properly define Uq[sl(m|n)(1)] and Uq[osp(2|2n)(1)]. We present a general technique for deriving the spectral-parameter-dependent R matrices from quantum affine superalgebras. We determine the R matrices for the type I affine superalgebra Uq[sl(m|n)(1)] in various representations, thereby deriving new solutions of the spectral-parameter-dependent Yang-Baxter equation. In particular, because this algebra possesses one-parameter families of finite-dimensional irreps, we are able to construct R matrices depending on two additional spectral-parameter-like parameters, providing generalizations of the free fermion model.

REALIZATION OF FRT ALGEBRA RELATED TO A COLORED BRAID GROUP REPRESENTATION

1994 ◽  
Vol 09 (29) ◽  
pp. 2733-2743 ◽  
Author(s):  
B. BASU-MALLICK
Keyword(s):  
Braid Group ◽  
Group Representation ◽  
Toda Chain ◽  
Baxter Equation ◽  
Color Parameter ◽  
Triangular Matrices ◽  
Explicit Realization ◽  
Lower Triangular ◽  
Parameter Dependent ◽  
Lower Triangular Matrices

A colored braid group representation (CBGR) is constructed by using some modified universal ℛ-matrix associated with U q( gl (2)) quantized algebra. Explicit realization of Faddeev–Reshetikhin–Takhtajan (FRT) algebra, involving color parameter dependent upper and lower triangular matrices, is built up for this CBGR and subsequently applied to generate nonadditive type solutions of quantum Yang–Baxter equation. Rational limit of such solutions interestingly yields 'colored' extension of known Lax operators associated with lattice nonlinear Schrödinger model and Toda chain.

scholarly journals Quantum entanglement, supersymmetry, and the generalized Yang-Baxter equation

2020 ◽  
Vol 20 (1&2) ◽  
pp. 37-64
Author(s):  
Pramod Padmanabhan ◽  
Fumihiko Sugino ◽  
Diego Trancanelli
Keyword(s):  
Quantum Entanglement ◽  
Communication Protocol ◽  
Quantum Information Theory ◽  
Entangled States ◽  
Baxter Equation ◽  
Classical Communication ◽  
Separable States ◽  
Qubit System ◽  
Large Families ◽  
Parameter Dependent

Entangled states, such as the Bell and GHZ states, are generated from separable states using matrices known to satisfy the Yang-Baxter equation and its generalization. This remarkable fact hints at the possibility of using braiding operators as quantum entanglers, and is part of a larger speculated connection between topological and quantum entanglement. We push the analysis of this connection forward, by showing that supersymmetry algebras can be used to construct large families of solutions of the spectral parameter-dependent generalized Yang-Baxter equation. We present a number of explicit examples and outline a general algorithm for arbitrary numbers of qubits. The operators we obtain produce, in turn, all the entangled states in a multi-qubit system classified by the Stochastic Local Operations and Classical Communication protocol introduced in quantum information theory.

scholarly journals TWISTED QUANTUM AFFINE ALGEBRAS AND SOLUTIONS TO THE YANG-BAXTER EQUATION

1996 ◽  
Vol 11 (19) ◽  
pp. 3415-3437 ◽  
Author(s):  
GUSTAV W. DELIUS ◽  
MARK D. GOULD ◽  
YAO-ZHONG ZHANG
Keyword(s):  
Lie Algebras ◽  
Spectral Parameter ◽  
Baxter Equation ◽  
Affine Lie Algebras ◽  
Quantum Affine Algebras ◽  
Enveloping Algebras ◽  
Quantized Enveloping Algebras ◽  
Affine Algebras ◽  
Parameter Dependent

We construct spectral-parameter-dependent R matrices for the quantized enveloping algebras of twisted affine Lie algebras. These give new solutions to the spectral-parameter-dependent quantum Yang-Baxter equation.

scholarly journals Parameter-dependent associative Yang–Baxter equations and Poisson brackets

2014 ◽  
Vol 11 (09) ◽  
pp. 1460036 ◽  
Author(s):  
Alexander Odesskii ◽  
Vladimir Rubtsov ◽  
Vladimir Sokolov
Keyword(s):  
General Class ◽  
Baxter Equation ◽  
Poisson Brackets ◽  
Poisson Structures ◽  
One Dimensional ◽  
All Solutions ◽  
Parameter Dependent

We discuss associative analogues of classical Yang–Baxter equation (CYBE) meromorphically dependent on parameters. We discover that such equations enter in a description of a general class of parameter-dependent Poisson structures and double Lie and Poisson structures in sense of Van den Bergh. We propose a classification of all solutions for one-dimensional associative Yang–Baxter equations (AYBE).

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