Birman-Wenzl-Murakami Algebra, Topological parameter and Berry phase

TL;DR

This paper presents a matrix representation of the Birman-Wenzl-Murakami algebra, constructs unitary matrices via Yang-Baxterization, and explores the relationship between a topological parameter and Berry phase in the system.

Contribution

It introduces a new (3x3)-matrix representation of the BWM algebra and links the topological parameter to Berry phase through a constructed Hamiltonian.

Findings

Unitary matrices generated from BWM algebra via Yang-Baxterization.

Berry phase is related to the topological parameter d.

Hamiltonian constructed from the unitary matrix exhibits topological properties.

Abstract

In this paper, a (3\times3)-matrix representation of the Birman-Wenzl-Murakami(BWM) algebra has been presented. Based on which, unitary matrices (A(\theta,\phi_1,\phi_2), B(\theta,\phi_1,\phi_2)) are generated via the Yang-Baxterization approach. A hamiltonian is constructed from the unitary (B(\theta,\phi)) matrix. We then study the Berry phase of the Yang-Baxter system and find the topological parameter d has relationship with berry phase.