A 9 × 9 Matrix Representation of Birman—Wenzl—Murakami Algebra and Berry Phase in Yang—Baxter System
Lidan Gou, Kang Xue, Gangcheng Wang
We present a 9 × 9 S-matrix and E-matrix. A representation of specialized Birman—Wenzl—Murakami algebra is obtained. Starting from the given braid group representation S-matrix, we obtain the trigonometric solution of Yang-Baxter equation. A unitary matrix Ř(x, ϕ 1 ,ϕ 2 ) is generated via the Yang—Baxterization approach. Then we construct a Yang—Baxter Hamiltonian through the unitary matrix Ř(x, ϕ 1 ,ϕ 2 ). Berry phase of this Yang—Baxter system is investigated in detail.
Communications in Theoretical Physics•Feb 1, 2011•5 citations