Spin-charge separation for paired Dirac fermions in $(1+1)$ dimensions

TL;DR

This paper explores how Dirac fermions coupled to a complex pairing field exhibit spin-charge separation in (1+1) dimensions, revealing emergent gauge couplings and symmetry-breaking phenomena that distinguish spin and charge degrees of freedom.

Contribution

It develops a mathematical framework for understanding spin-charge separation in Dirac fermions with pairing fields, including theorems on generic features of this phenomenon.

Findings

Spin-charge separation occurs with broken $U(1)$ symmetry.

Emergent spin-dependent gauge coupling binds spin and charge.

Signaling of spin-charge separation by $ ext{PT}$-symmetry breaking.

Abstract

We study Dirac fermions at finite density coupled to a complex pairing field assumed to obey scalar field theory with quartic self-repulsion. The bulk of our work develops the mathematics that elucidates the propagation of fermionic excitations in such systems as independent spin (boosts) and charge (fermion number) degrees of freedom. A necessary ingredient is the presence of broken $U(1)$ symmetry in the pairing field and decoupling of its density and phase. In the fermion sector, these elements give rise to an emergent spin-dependent gauge coupling which binds in-vacuum spin and charge into elementary fermions, while driving proliferation of unbound spin and charge for finite condensation in the pairing field. Notably, the onset of spin-charge separation is signaled by $\mathcal{P} \mathcal{T}$-symmetry breaking and decoupling of spin components under Lorentz transformations. Our investigation concludes with two theorems that identify generic features of spin-charge separation in such systems.