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Spin wave Feynman diagram vertex computation packageSpin 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.
Studying Quantum Magnets Using Ineracting Spin Wave TheoryA magnon is a quantized magnetic excitation hosted in a condensed matter state caused by deviations of the electron spin. Quantum fluctuations of the magnetic wave results in a quantized spin wave. Using spin wave theory we present a derivation of the interaction that describes magnons in a 3D ferromagnetic crystal lattice and a 2D antiferromagnetic crystal. We use both the Holstein-Primakoff and Dyson-Maleev bosonization transformation scheme. As in the literature, we find higher order interaction terms within the Hamiltonian. We present a derivation of these interaction terms and subsequent representation from a Feynman diagram approach.