Understanding Symmetry Breaking in Twisted Bilayer Graphene from Cluster Constraints

Abstract

Twisted bilayer graphene is an exciting platform for exploring correlated quantum phases, extremely tunable with respect to both the single-particle bands and the interaction profile of electrons. Here, we investigate the phase diagram of twisted bilayer graphene as described by an extended Hubbard model on the honeycomb lattice with two fermionic orbitals (valleys) per site. Besides the special extended {\it cluster interaction} $Q$, we incorporate the effect of gating through an onsite Hubbard-interaction $U$. Within Quantum Monte Carlo (QMC), we find valence-bond-solid, Néel-valley antiferromagnetic or charge-density wave phases. Further, we elucidate the competition of these phases by noticing that the cluster interaction induces an exotic constraint on the Hilbert space, which we dub {\it the cluster rule}, in analogy to the famous pyrochlore spin-ice rule. Formulating the perturbative Hamiltonian by projecting into the cluster-rule manifold, we perform exact diagonalization and construct the fixed-point states of the observed phases. Finally, we compute the local electron density patterns as signatures distinguishing these phases, which could be observed with scanning tunneling microscopy. Our work capitalizes on the notion of cluster constraints in the extended Hubbard model of twisted bilayer graphene, and suggests a scheme towards realization of several symmetry-breaking insulating phases in a twisted-bilayer graphene sheet.

10 pages, 6 figures

References in corpus (10)

• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Quantum critical behavior in magic-angle twisted bilayer graphene
• Quantum textures of the many-body wavefunctions in magic-angle graphene
• Global Phase Diagram of the Normal State of Twisted Bilayer Graphene
• Extended dynamical mean-field study of the Hubbard model with long range interactions
• Imaging inter-valley coherent order in magic-angle twisted trilayer graphene
• Spectroscopy of Twisted Bilayer Graphene Correlated Insulators
• Detecting symmetry breaking in magic angle graphene using scanning tunneling microscopy
• Level spectroscopy in a two-dimensional quantum magnet: Linearly dispersing spinons at the deconfined quantum critical point
• Chern-insulator phases and spontaneous spin and valley order in a moiré lattice model for magic-angle twisted bilayer graphene

Cited by in corpus (3)

• Moiré optical phonons dancing with heavy electrons in magic-angle twisted bilayer graphene
• Coexistence of ergodic and non-ergodic behavior and level spacing statistics in a one-dimensional model of a flat band superconductor
• How quantum fluctuations freeze a classical liquid and then melt it into a topological one