On representation of the t-J model via spin-charge variables

TL;DR

This paper demonstrates that the t-J Hamiltonian cannot generally be simplified to a form involving independent spin and charge variables, using superalgebra representations and path integral methods.

Contribution

It provides a proof that the t-J model cannot be reduced to a simple spin-charge separated form using superalgebra techniques.

Findings

Hubbard operators identified with su(2|1) superalgebra generators

SU(2|1) path integral representation derived

t-J Hamiltonian not reducible to independent spin and charge variables

Abstract

We show that the t-J Hamiltonian is not in general reduced to H(S,f), where S and f stand for independent ([S,f]=0) SU(2) (spin) generators and spinless fermionic (hole) field, respectively. The proof is based upon an identification of the Hubbard operators with the generators of the su(2|1) superalgebra in the degenerate fundamental representation and ensuing SU(2|1) path integral representation of the partition function.