arXiv subjects

Guijiao Du

Publications and source records attributed to Guijiao Du.

3 recordsLinked to original sources

arXiv2011

Birman-Wenzl-Murakami Algebra and the Topological Basis

In this paper, we use entangled states to construct 9x9-matrix representations of Temperley-Lieb algebra (TLA), then a family of 9x9-matrix representations of Birman-Wenzl-Murakami algebra (BWMA) have been presented. Based on which, three topological basis states have been found. And we apply topological basis states to recast nine-dimensional BWMA into its three-dimensional counterpart. Finally, we find the topological basis states are spin singlet states in special case.

quant-ph↗

arXiv2010

Quantum tunneling effect and quantum Zeno effect in a Topological system

A spin interaction Hamiltonian for topological basis is constructed in this paper. When we select proper parameters, this Hamiltonian system can be simulated by a quantum double well potential system. If the parameter $Δ=0$, the topological system is equivalent to two independent quantum wells. If the parameter $Δ\neq 0$, the system is equivalent to a double well potential with finite potential barrier. The quantum tunneling effect and quantum Zeno effect for this topological system are investigated in detail.

quant-ph↗

arXiv2010

Yang-Baxter $\breve{R}$ matrix, Entanglement and Yangian

We present a method to construct "X" form unitary Yang-Baxter $\breve{R}$ matrices, which act on the tensor product space $V_{i}^{j_{1}}\otimes V_{i+1}^{j_{2}}$. We can obtain a set of entangled states for $(2j_{1}+1)\times (2j_{2}+1)$-dimensional system with these Yang-Baxter $\breve{R}$ matrices. By means of Yang-Baxter approach, a $8\times 8$ Yang-Baxter Hamiltonian is constructed. Yangian symmetry and Yangian generators as shift operators for this Yang-Baxter system are investigated in detail.

math-ph↗