Spin-1/2 operators exactly mapped to spinful canonical Fermi operators present in two bands

TL;DR

This paper extends the exact transformation of quantum spin-1/2 operators into spinful Fermi operators to include two-band systems in one dimension, broadening the applicability of the Jordan-Wigner transformation.

Contribution

It introduces an exact mapping of spin-1/2 operators to two-band spinful Fermi operators in 1D using an extended Jordan-Wigner transformation.

Findings

Exact two-band spinful Fermi representation of spin-1/2 operators in 1D.

Extension of Jordan-Wigner transformation to multi-band systems.

Potential applications in modeling complex quantum systems.

Abstract

Recently it has been shown that the quantum spin-1/2 spin operators can be exactly transformed not only in spinless, but also in spinful canonical Fermi operators in 1D [\cite{JW1}], and 2D [\cite{JW2}] as well. In this paper, using the same technique based on an extended Jordan-Wigner transformation, we show in 1D, that the quantum spin-1/2 operators can be exactly transformed also in spinful canonical Fermi operators of spin-1/2 fermions that are belong to two bands.