The application of the Schur-Weyl duality in the one-dimensional Hubbard model

TL;DR

This paper demonstrates how Schur-Weyl duality can be applied to simplify the eigenproblem in the one-dimensional Hubbard model at half-filling, reducing computational complexity.

Contribution

It introduces a novel application of Schur-Weyl duality to the Hubbard model, enabling a reduction in the eigenproblem's dimension for half-filled systems.

Findings

Significant reduction in eigenproblem dimension

Application of dual groups in spin and pseudo-spin spaces

Simplified calculations for the Hubbard model

Abstract

We present the application of the Schur-Weyl duality in the one-dimensional Hubbard model in the case of half-filled system of any numer of atoms. We replace the actions of the dual symmetric and unitary groups in the whole Hilbert space by the actions of the dual groups in the spin and pseudo-spin spaces. The calculations significantly reduce the dimension of the eigenproblem of the one-dimensional Hubbard model.