Exact Transformation for Spin-Charge Separation of Spin-half Fermions without Constraints

TL;DR

This paper introduces an exact local transformation that maps a fermionic system to a boson-fermion system, revealing new insights into spin-charge separation and localization in the Hubbard model.

Contribution

It provides a novel exact transformation for spin-half fermions into bosons and spinless fermions without constraints, applied to the Hubbard model.

Findings

Charge tends to remain localized at large U values.

The transformation preserves all symmetries of the Hubbard model.

Approximate localized charge solutions naturally emerge.

Abstract

We demonstrate an exact local transformation which maps a purely Fermionic manybody system to a system of spinfull Bosons and spinless Fermions, demonstrating a possible path to a non-Fermi liquid state. We apply this to the half-filled Hubbard model and show how the transformation maps the ordinary spin half Fermionic degrees of freedom exactly and without introducing Hilbert space constraints to a charge-like ``quasicharge'' fermion and a spin-like ``quasispin'' Boson while preserving all the symmetries of the model. We present approximate solutions with localized charge which emerge naturally from the Hubbard model in this form. Our results strongly suggest that charge tends to remain localized for large values of the Hubbard U.