Zero energy eigenstates ψ 0 ( θ ) of the twisted bilayer graphene Hamiltonian at the Dirac point show a high sensitivity to the twist angle θ near the magic angles where the effective Fermi velocity vanishes. We use information theory markers, like fidelity-susceptibility and entanglement entropy of the reduced density matrix to the layer sector, to capture this quantum criticality of zero modes at magic twist angles. • This article contributes to unravel the magic behind the electronic properties and exotic quantum states of twisted bilayer graphene. • The quantum criticality of zero modes at magic twist angles is revealed by fidelity and entanglement measures, as an alternative complement to the usual Fermi velocity, conductivity and band flattening characteristics. • We provide plots of fidelity, entanglement and interlayer hopping probabilities of conduction and valence zero modes as a function of the twist angle, where magic angles are conspicuous.
We describe a method for creating twist defects in the honeycomb Floquet code of Hastings and Haah. In particular, we construct twist defects at the endpoints of condensation defects, which are built by condensing emergent fermions along one-dimensional paths. We argue that the twist defects can be used to store and process quantum information fault tolerantly, and demonstrate that, by preparing twist defects on a system with a boundary, we obtain a planar variant of the
Z2 Floquet code. Importantly, our construction of twist defects maintains the connectivity of the hexagonal lattice, requires only 2-body measurements, and preserves the three-round period of the measurement schedule. We furthermore generalize the twist defects to
ZN Floquet codes defined on
N-dimensional qudits. As an aside, we use the
ZN Floquet codes and condensation defects to define Floquet codes whose instantaneous stabilizer groups are characterized by the topological order of certain Abelian twisted quantum doubles.