Topological Basis Associated with B-M-W algebra: Two Spin-1/2 Realization
arXiv:1404.4794 · doi:10.1016/j.physleta.2014.10.037
Abstract
In this letter, we study the two-spin-1/2 realization for the Birman-Murakami-Wenzl (B-M-W) algebra and the corresponding Yang-Baxter matrix. Based on the two-spin-1/2 realization for the B-M-W algebra, the three-dimensional topological space, which is spanned by topological basis, is investigated. By means of such topological basis realization, the four-dimensional Yang-Baxter can be reduced to Wigner function with . The entanglement and Berry phase in the spectral parameter space are also explored. The results show that one can obtain a set of entangled basis via Yang-Baxter matrix acting on the standard basis, and the entanglement degree is maximum when the turns to the braiding operator.
arXiv comment5 pages
References in corpus (15)
- Entanglement of Formation of an Arbitrary State of Two Qubits
- Non-Abelian Anyons and Topological Quantum Computation
- Encoding a qubit in an oscillator
- Braiding Operators are Universal Quantum Gates
- The two-eigenvalue problem and density of Jones representation of braid groups
- Braiding transformation, entanglement swapping and Berry phase in entanglement space
- Optical Simulation of Yang-Baxter Equation
- Direct Experimental Simulation of the Yang-Baxter Equation
- Localization of unitary braid group representations
- Quantum spin chains of Temperley-Lieb type: periodic boundary conditions, spectral multiplicities and finite temperature
- Spin coherent states in NMR quadrupolar system: experimental and theoretical applications
- Symmetries of spin systems and Birman-Wenzl-Murakami algebra
- Thermal and magnetic properties of integrable spin-1 and spin-3/2 chains with applications to real compounds
- Quantum entanglement, unitary braid representation and Temperley-Lieb algebra
- Bethe ansatz for the Temperley-Lieb spin-chain with integrable open boundaries