On Quantum Groups in the Hubbard Model with Phonons

TL;DR

This paper derives the Hamiltonian for an extended Hubbard model with quantum group symmetry, revealing that superconducting SUq(2) symmetry is only valid in one dimension and requires specific conditions like half filling.

Contribution

It provides a detailed derivation of the Hamiltonian with quantum group symmetry in D-dimensional lattices and clarifies the conditions under which superconducting symmetry holds.

Findings

Superconducting SUq(2) symmetry exists only in one-dimensional systems.

Higher-order fermionic terms are necessary for quantum symmetry in the Hamiltonian.

Quantum symmetry is maintained at half filling without local electron-phonon coupling.

Abstract

The correct Hamiltonian for an extended Hubbard model with quantum group symmetry as introduced by A. Montorsi and M. Rasetti is derived for a D-dimensional lattice. It is shown that the superconducting SUq(2) holds as a true quantum symmetry only for D = 1 and that terms of higher order in the fermionic operators in addition to phonons are required for a quantum symmetric hamiltonian. The condition for quantum symmetry is "half filling" and there is no local electron-phonon coupling. A discussion of Quantum symmetries in general is given in a formalism that should be readily accessible to non Hopf-algebraists.