Introduction to the Bethe Ansatz III

Michael Karbach; Kun Hu; Gerhard Muller

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Introduction to the Bethe Ansatz III

Michael Karbach·Kun Hu·Gerhard Muller

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Abstract

Having introduced the magnon in part I and the spinon in part II as the relevant quasi-particles for the interpretation of the spectrum of low-lying excitations in the one-dimensional (1D) s=1/2 Heisenberg ferromagnet and antiferromagnet, respectively, we now study the low-lying excitations of the Heisenberg antiferromagnet in a magnetic field and interpret these collective states as composites of quasi-particles from a different species. We employ the Bethe ansatz to calculate matrix elements and show how the results of such a calculation can be used to predict lineshapes for neutron scattering experiments on quasi-1D antiferromagnetic compounds. The paper is designed as a tutorial for beginning graduate students. It includes 11 problems for further study.

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Michael Karbach, Kun Hu, Gerhard Muller. 2000-08-01. Introduction to the Bethe Ansatz III. https://arxiv.org/abs/cond-mat/0008018

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