Abstract
This chapter gives the mathematical details of the calculation of the ground state energy of the spin-1/2 linear chain with antiferromagnetic nearest neighbour exchange. Although the form of the ground-state wave function had been given by Bethe using the Bethe Ansatz, as described in the previous chapter, it was several years before Hulthén was able to use it to calculate the ground-state energy. The procedure involves setting up an integral equation for a function f. Although f does not have a simple physical significance, the complete wave function is made up of a superposition of phase-shifted plane waves with wave vector k. f is related to the rate of change of the density of the distribution k. Once the fundamental integral equation has been derived it is solved by Fourier transform. Finally the solution f is used to find the antiferromagnetic ground-state energy.
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Parkinson, J.B., Farnell, D.J. (2010). The Antiferromagnetic Ground State. In: An Introduction to Quantum Spin Systems. Lecture Notes in Physics, vol 816. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13290-2_4
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DOI: https://doi.org/10.1007/978-3-642-13290-2_4
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