On the application of Jucys-Murphy operators in the Hubbard model

TL;DR

This paper applies Jucys-Murphy operator techniques to diagonalize the 1D Hubbard model efficiently, using Young orthogonal basis and group symmetries, notably reducing the eigenproblem size in specific cases.

Contribution

It introduces a novel application of Jucys-Murphy operators and Young basis to simplify the Hubbard model diagonalization process.

Findings

Reduced eigenproblem size in the Hubbard model

Effective use of symmetric group representations

Application to attractive half-filled rings

Abstract

The operator techniques based on the Jucys-Murphy operators were applied in the procedure of an immediate diagonalization of the one-dimensional Hubbard model. The Young orthogonal basis was given by the irreducible basis of the symmetric group acting on the set of nodes of the magnetic chain. The example of the attractive Hubbard model at the half-filled magnetic rings case was considered where the group $SU(2)\times SU(2)$ acts within the spin and pseudo-spin space. These techniques significantly reduced size of the eigenproblem of the Hubbard Hamiltonian.