SO(8) Fermion Dynamical Symmetry and Strongly-Correlated Quantum Hall States in Monolayer Graphene

TL;DR

This paper introduces an SO(8) fermion dynamical symmetry formalism to analyze strongly-correlated quantum Hall states in monolayer graphene, extending existing models and providing analytical solutions for complex collective states.

Contribution

It develops an SO(8) symmetry framework that generalizes quantum Hall ferromagnetism in graphene, enabling analytical many-body solutions and a unified description of competing broken symmetries.

Findings

SO(8) symmetry includes pairing and particle-hole generators.

Extension of SU(4) symmetry to SO(8) for quantum Hall states.

Analytical solutions for collective states with broken symmetries.

Abstract

A formalism is presented for treating strongly-correlated graphene quantum Hall states in terms of an SO(8) fermion dynamical symmetry that includes pairing as well as particle--hole generators. The graphene SO(8) algebra is isomorphic to an SO(8) algebra that has found broad application in nuclear physics, albeit with physically very different generators, and exhibits a strong formal similarity to SU(4) symmetries that have been proposed to describe high-temperature superconductors. The well-known SU(4) symmetry of quantum Hall ferromagnetism for single-layer graphene is recovered as one subgroup of SO(8), but the dynamical symmetry structure associated with the full set of SO(8) subgroup chains extends quantum Hall ferromagnetism and allows analytical many-body solutions for a rich set of collective states exhibiting spontaneously-broken symmetry that may be important for the low-energy physics of graphene in strong magnetic fields. The SO(8) symmetry permits a natural definition of generalized coherent states that correspond to symmetry-constrained Hartree--Fock--Bogoliubov solutions, or equivalently a microscopically-derived Ginzburg--Landau formalism, exhibiting the interplay between competing spontaneously broken symmetries in determining the ground state.