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Journal of Physics Condensed Matter

A comment on 'The classical limit for the Holstein-Primakoff representation in the soliton theory of Heisenberg chains'

Алексей Владимирович Маханьков, Vladmir G. Makhankov

Published Jul 23, 1990• 0 citations
Publisher

Abstract

Skrinjar and co-workers (see ibid., vol.1, p.725, 1989) used a Holstein-Primakoff operator method to obtain a classical Hamiltonian. It is shown that the same Hamiltonian can be derived directly via averaging over spin coherent states, so the former contains no extra information in the limit s to infinity .
DOI
10.1088/0953-8984/2/29/013

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The product ( delta s x ) 2 ( delta s y ) 2 is computed where ( delta s x,y ) 2 =(s x,y 2 )-(s x,y ) 2 ; averaging is performed in the coherent spin-state representation given by Radcliffe (1971). After applying the Holstein- Primakoff transformation s - =(2s) 1 2/a Dagger , s + =(2s) 1 2/a and mu = alpha /(2s) 1 2/, and putting s to infinity one proceeds from Radcliffe space into the Glauber space. After this procedure the product ( delta s x ) 2 ( delta s y ) 2 becomes ( delta x) 2 ( delta p) 2 . Using the Jackiw equation it is shown that the function mod mu =0> is the only one which minimizes the uncertainty product, for every s.