Spin-charge rotating local reference frames: a unified U(2)=U(1)xSU(2) approach to the interacting electrons

TL;DR

This paper presents a unified gauge-theoretic framework for the Hubbard model, describing electrons as composite objects with charge and spin degrees of freedom governed by U(1) and SU(2) gauge fields, revealing topological effects.

Contribution

It introduces a spin-charge unifying approach using local gauge transformations, linking topological structures to electron interactions in the Hubbard model.

Findings

Electrons are described as composites with gauge fields.

Effective action includes topological theta terms.

Topological structure influences electron behavior.

Abstract

A spin-charge unifying description for the Hubbard model based on the time dependent local gauge transformations is developed. The collective variables for charge and spin are isolated in the form of the space-time fluctuating U(1) phase field and rotating spin quantization axis governed by the SU(2) symmetry, respectively. As a result interacting electrons appear as a composite objects consisting of bare fermions with attached U(1) and SU(2) gauge fields. We elaborate on the microscopic origins of the effective action with the Coulomb interaction that contain topological theta terms. Furthermore, we unravel the link between non-trivial multiply-connected topological structure of the U(2)=U(1)$\otimes$SU(2) configurational space for gauge fields and the instanton contribution to the statistical sum.