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Journal of the Physical Society of Japan

Quantized Bogoliubov Transformationand the Holon-Spinon Operator Formalism

T. Suzuki

Published Nov 15, 1991• 0 citations
Publisher

Abstract

It is shown that the method proposed by Nakajima to describe the spinon and holon degrees of freedom in strongly correlated electron systems is obtained as a special case of the quantized Bogoliubov transformation developed for a description of the nuclear pairing field.
DOI
10.1143/jpsj.60.3612

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The present paper attempts to give independent descriptions of the collective degrees of freedom of nuclei such as the monopole and quadrupole ones in order to avoid the seniority mixing problem. This is done by the operatorized Bogoliubov transformation (OBT) which separates the degree of freedom from the rest described by the seniority particle operator which is not coupling to the pairs, and in terms of which the independent pair is composed. The OBT is derived in such a way that it can be generalized easily to include a new kind of “seniority particle operator” neither coupling to the nor to the pairs. In terms of this new particle operator the independent pair or the independent odd particle in odd nuclei is constructed.
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Spinons are among the generic excitations in one-dimensional spin systems; they can be massless or massive. The quantitative description of massive spinons poses a considerable challenge in spite of various variational approaches. We show that a representation in terms of hopping and Bogoliubov spinon processes, which we call ``spinon-pair'' operators, and their combination is possible. We refer to such a representation as second quantized form. Neglecting terms which change the number of spinons yields the variational results. Treating the bilinear and quartic terms by continuous unitary transformations leads to considerably improved results. Thus, we provide the proof of principle that systems displaying massive spinons as elementary excitations can be treated in second quantization based on spinon-pair representation.