Emergent symmetries in the global phase diagram of two-dimensional extended honeycomb-Hubbard model

Massless Dirac fermions realized as low-energy emergent quasiparticles in carbon-based monolayer honeycomb membrane constitute an ideal platform to address competing phases, metallic quantum criticality, and emergent symmetries at the infrared unstable quantum critical points. I will show that the global phase diagram of two-dimensional extended honeycomb-Hubbard model of interacting massless Dirac fermions is governed by altogether five quantum critical points. They display confluence among antiferromagnet, quantum Spin Hall insulator, charge-density-wave, Kekule valence bond solids, and s-wave pairing, for example, and restoration of enlarged symmetry among them. These outcomes will then be substantiated by representative cuts of the global phase diagram in the presence of onsite Hubbard and nearest-neighbor interactions, for example. I will also discuss the role of the long-range tail of the Coulomb interaction on the global phase diagram of this system.