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    Spin wave Feynman diagram vertex computation package

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    Authors
    Price, Alexander
    Javernick, Philip
    Datta, Trinanjan
    Issue Date
    2016-03-14
    URI
    http://hdl.handle.net/10675.2/604241
    
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    Abstract
    Spin wave theory is a well-established theoretical technique that can correctly predict the physical behavior of ordered magnetic states. However, computing the effects of an interacting spin wave theory incorporating magnons involve a laborious by hand derivation of Feynman diagram vertices. The process is tedious and time consuming. Hence, to improve productivity and have another means to check the analytical calculations, we have devised a Feynman Diagram Vertex Computation package. In this talk, we will describe our research group’s effort to implement a Mathematica based symbolic Feynman diagram vertex computation package that computes spin wave vertices. Utilizing the non-commutative algebra package NCAlgebra as an add-on to Mathematica, symbolic expressions for the Feynman diagram vertices of a Heisenberg quantum antiferromagnet are obtained. Our existing code reproduces the well-known expressions of a nearest neighbor square lattice Heisenberg model. We also discuss the case of a triangular lattice Heisenberg model where non collinear terms contribute to the vertex interactions.
    Affiliation
    Department of Chemistry and Physics
    Description
    Presentation given at the American Physical Society March Meeting 2016 on Monday, March 14, 2016
    Collections
    Department of Chemistry and Physics: Student Research and Presentations

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