Quantum Symmetry of Hubbard Model Unraveled

TL;DR

This paper explores the quantum symmetries in extended Hubbard models, revealing their origin from classical SO(4) symmetry and extending to quantum groups, with implications for one-dimensional systems.

Contribution

It introduces a framework connecting classical SO(4) symmetry to quantum symmetries in Hubbard models, including models with additional parameters and symmetries beyond half filling.

Findings

Superconducting quantum symmetries derive from classical SO(4) symmetry.

Quantum group extensions are restricted to one dimension.

A general model with symmetric interactions and SO(4) symmetry is explicitly constructed.

Abstract

Superconducting quantum symmetries in extended single-band 1-dimensional Hubbard models are shown to originate from the classical (pseudo-)spin SO(4) symmetry of a class of models of which the standard Hubbard model is a special case. Extending the notion of symmetry to include quantum groups allows us to introduce extra parameters but the corresponding quantum symmetric models are restricted to one dimension. All models discussed are related by generalized Lang-Firsov transformations, some have symmetries away from half filling. The most general model with symmetric next-neighbour interaction terms and classical SO(4) symmetry is given explicitly.