Title:- Emergent symmetry in the renormalization group flow trajectories of extended Hubbard model in Bernal bilayer graphene

Abstract:- Due to quadratic touching of filled valence and empty conduction bands, yielding a finite density of states at low energies, Bernal stacked bilayer graphene constitutes an ideal platform to capture asymptotic freedom and BCS instabilities in the global phase diagram of extended Hubbard model for an interacting electronic fluid therein. Performing a leading order renormalization group (RG) analysis, we show that when an extended honeycomb-Hubbard model causes BCS instabilities of the disordered electronic ground state toward the nucleation of various competing ordered states, internal symmetry among distinct microscopic phases emerges along the RG flow trajectories. Paradigmatic cases include, for example, symmetry restoration between the layer antiferromagnet and Kekule (a) current as well as (b) pair-density-wave orders, enriching the emergent SO(5) among them with the `color degeneracy'. We map out all such RG flow trajectories through which the system can develop ordered states and the restoration of emergent enlarged symmetries along such RG paths. We also identify the footprint of such high-symmetry RG flow trajectories on various instructive cuts of the microscopic extended Honeycomb-Hubbard model on Bernal bilayer graphene.