Jordan-Wigner transformation constructed for spinful fermions at S=1/2 spins in one dimension

TL;DR

This paper introduces an exact Jordan-Wigner transformation for one-dimensional spin-1/2 systems with spinful fermions, featuring adjustable parameters to connect various spin and fermionic models.

Contribution

It presents a generalized Jordan-Wigner transformation with free parameters, expanding the ability to relate spin models to spinful fermionic models in one dimension.

Findings

Transformation is exact and parameterized.

Enables broad connections between spin and fermionic models.

Facilitates new analytical approaches in 1D quantum systems.

Abstract

An exact Jordan-Wigner type of transformation is presented in 1D connecting spin-1/2 operators to spinful canonical Fermi operators. The transformation contains two free parameters allowing a broad interconnection possibility in between spin models and fermionic models containing spinful Fermi operators.