Twisted Materials as Many Body Hamiltonian “Simulators”
We will show that twisted bilayer and trilayer graphene can be understood as a topological heavy fermion problem where the “f” electron is made out of thousands of carbon pz orbitals while the c electron is that of untwisted bilayer graphene with heavily renormalized bands. This exact mapping allows for a model where the interaction becomes local. The presence of Hubbard bands, cascades between different quantum flavors, kondo like peaks that have puzzled the field can be naturally explained in this way, as can be the renormalization of the large repulsive coulomb necessary to obtain superconductivity. We then show that this is but one of the many models that can be realized in different classes of twisting: depending on which lattice you twist, and at which point your band minimum or maximum is, one can obtain a variety of many body Hamiltonians - from those of fractional Chern insulators to those of t-J models, spin liquids, and many others. Our recent database of twistable monolayers promises candidates for each of these systems.
Host: Leonid Glazman