Towards the hidden symmetry in Coulomb interacting twisted bilayer graphene: renormalization group approach

TL;DR

This paper develops a two-stage renormalization group approach to connect the continuum Hamiltonian of twisted bilayer graphene at short scales to the effective narrow band Hamiltonian at long scales, revealing hidden symmetries and residual correlations.

Contribution

It introduces a novel two-stage renormalization group method that links short-scale continuum models to long-scale narrow band models in twisted bilayer graphene, highlighting hidden symmetries.

Findings

Suppression of certain tunneling ratios approaching the chiral limit.

Quantification of residual correlations within the narrow band.

Identification of softening collective modes indicating hidden symmetry.

Abstract

We develop a two stage renormalization group which connects the continuum Hamiltonian for twisted bilayer graphene at length scales shorter than the moire superlattice period to the Hamiltonian for the active narrow bands only which is valid at distances much longer than the moire period. In the first stage, the Coulomb interaction renormalizes the Fermi velocity and the interlayer tunnelings in such a way as to suppress the ratio of the same sublattice to opposite sublatice tunneling, hence approaching the so-called chiral limit. In the second stage, the interlayer tunneling is treated non-perturbatively. Via a progressive numerical elimination of remote bands the relative strength of the one-particle-like dispersion and the interactions within the active narrow band Hamiltonian is determined, thus quantifying the residual correlations and justifying the strong coupling approach in the final step. We also calculate exactly the exciton energy spectrum from the Coulomb interactions projected onto the renormalized narrow bands. The resulting softening of the collective modes marks the propinquity of the enlarged ("hidden") $U(4)\times U(4)$ symmetry in the magic angle twisted bilayer graphene.