Massive spinons in $S=1/2$ spin chains: spinon-pair operator representation

TL;DR

This paper introduces a second quantized spinon-pair operator framework to effectively describe massive spinons in one-dimensional $S=1/2$ spin chains, improving upon previous variational methods.

Contribution

It develops a novel spinon-pair operator representation and applies continuous unitary transformations to enhance the description of massive spinons.

Findings

Second quantized spinon-pair representation is feasible.

Improved variational results with continuous unitary transformations.

Proof-of-principle for treating massive spinons in second quantization.

Abstract

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.