Kekulé valence bond order in an extended Hubbard model on the honeycomb lattice, with possible applications to twisted bilayer graphene

Abstract

Using large-scale quantum Monte Carlo simulations, we exactly solve a model of Fermions hopping on the honeycomb lattice with cluster charge interactions, which has been proposed as an effective model with possible application to twisted bilayer graphene near half-filling. We find an interaction driven semimetal to insulator transition to an insulating phase consisting of a valence bond solid with Kekulé pattern. Finite size scaling reveals that the phase transition of the semimetal to Kekulé valence bond solid phase is continuous and belongs to chiral XY universality class.

4+1 pages, 4 figures

References in corpus (18)

• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
• Flat Bands in Slightly Twisted Bilayer Graphene
• Continuum Model of the Twisted Bilayer
• Electron fractionalization in two-dimensional graphenelike structures
• Topological Superconductivity in Twisted Multilayer Graphene
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• Numerical studies of confined states in rotated bilayers of graphene
• Model for Metal-Insulator Transition in Graphene Superlattices and Beyond
• Phases of a phenomenological model of twisted bilayer graphene
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Pairing symmetry of interacting fermions on twisted bilayer graphene superlattice
• Confinement transition of ${\mathbb{Z}}_2$ gauge theories coupled to massless fermions: emergent QCD${}_3$ and $SO(5)$ symmetry
• Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry
• Gauge-field-assisted Kekulé quantum criticality
• Correlation-Driven Dimerization and Topological Gap Opening in Isotropically Strained Graphene
• Fermion-induced quantum criticality with two length scales in Dirac systems
• Quantum criticality in the metal-superconductor transition of interacting Dirac fermions on a triangular lattice

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