Mapping spin-charge separation without constraints

TL;DR

This paper presents a new mapping of electron spin and charge degrees of freedom onto spinless fermions and local spins, preserving the Hilbert space size and satisfying the single occupancy constraint exactly, unlike previous methods.

Contribution

It derives a general mapping that exactly enforces the single occupancy condition of the t-J model without additional constraints, clarifying the role of pseudospin and providing a geometric spinor description.

Findings

The mapping preserves the four-state Hilbert space per site.

It explicitly distinguishes physical electron spin from pseudospin.

The mapped Hamiltonian couples spin and spinless fermion currents.

Abstract

The general form of a mapping of the spin and charge degrees of freedom of electrons onto spinless fermions and local `spin'-1/2 operators is derived. The electron Hilbert space is mapped onto a tensor productspin-charge Hilbert space. The single occupancy condition of the t-J model is satisfied exactly without the constraints between the operators required with slave particle methods and the size of the Hilbert space (four states per site) is conserved. The connection and distinction between the physical electron spin and the ``pseudospin'' used in these maps is made explicit. Specifically the pseudospin generates rotations both in spin space and particle-hole space. A geometric description (up to sign) is provided using two component spinors. The form of the mapped t-J Hamiltonian involves the coupling of spin and spinless fermion currents, as one expects.