Higher dimensional multiparameter unitary and nonunitary braid matrices: Even dimensions

@article{Abdesselam2007HigherDM,
  title={Higher dimensional multiparameter unitary and nonunitary braid matrices: Even dimensions},
  author={Boucif Abdesselam and Amitabha Chakrabarti and Vladimir Dobrev and S. G. Mihov},
  journal={Journal of Mathematical Physics},
  year={2007},
  volume={48},
  pages={103505-103505}
}
A class of (2n)2×(2n)2 multiparameter braid matrices are presented for all n(n⩾1). Apart from the spectral parameter θ, they depend on 2n2 free parameters mij(±), i,j=1,…,n. For real parameters, the matrices R(θ) are nonunitary. For purely imaginary parameters, they became unitary. Thus, a unification is achieved with odd dimensional multiparameter solutions presented before. 
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12 Citations
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Methods Citations
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12 Citations

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References

SHOWING 1-8 OF 8 REFERENCES

Higher dimensional unitary braid matrices: Construction, associated structures, and entanglements

We construct (2n)2×(2n)2 unitary braid matrices R for n⩾2 generalizing the class known for n=1. A set of (2n)×(2n) matrices (I,J,K,L) is defined. R is expressed in terms of their tensor products…

Canonical factorization and diagonalization of Baxterized braid matrices: Explicit constructions and applications

Braid matrices R(θ), corresponding to vector representations, are spectrally decomposed obtaining a ratio fi(θ)/fi(−θ) for the coefficient of each projector Pi appearing in the decomposition. This…

A nested sequence of projectors and corresponding braid matrices R̂(θ). 1. Odd dimensions

A basis of N2 projectors, each an N2×N2 matrix with constant elements, is implemented to construct a class of braid matrices R(θ), θ being the spectral parameter. Only odd values of N are considered…

Nested sequence of projectors. II. Multiparameter multistate statistical models, Hamiltonians, S-matrices

Our starting point is a class of braid matrices, presented in a previous paper, constructed on a basis of a nested sequence of projectors. Statistical models associated to such N2×N2 matrices for odd…

Braiding operators are universal quantum gates

This paper explores the role of unitary braiding operators in quantum computing. We show that a single specific solution R (the Bell basis change matrix) of the Yang–Baxter equation is a universal…

Yang-Baxter algebras, integrable theories and quantum groups

Small-scale anisotropy in stably stratified turbulence

In this paper, small-scale statistics in stably stratified turbulence is studied theoretically and numerically. Expressions for the spectra of the velocity correlation, density fluctuation and…

GHZ States, Almost-Complex Structure and Yang–Baxter Equation

The Bell matrix is defined to yield all the Greenberger–Horne–Zeilinger (GHZ) states from the product basis, proved to form a unitary braid representation and presented as a new type of solution of the quantum Yang–Baxter equation.