Critical behavior of fractionalized excitations in trimer model of twisted bilayer graphene

Moiré graphene systems provide an exciting platform to realize new physics, including a previously proposed suite of fractionalized excitations arising from fractional correlated insulating states at fractional fillings [1] of twisted bilayer graphene (TBG). However, rigorous analysis of the physics of quasiparticles has been difficult due to geometric frustration in the trimer model of TBG, arising in a ground state manifold with highly constrained local moves that still retains extensive entropy. In this work, we perform classical Monte Carlo simulations making use of the "pocket algorithm" [2] to achieve ergodicity with global updates even for highly frustrated models. We numerically evaluate critical exponents of monomer (1/3 charged quasiparticle) and trimer (electron) correlations to be 1/4 and 2, respectively, which is consistent with a proposed effective field theory. Furthermore, we investigate the confinement and restricted mobility of quasiparticles in the context of our numerical simulations and their implications for electronic transport in fractional fillings of twisted bilayer graphene.

[1] Mao et al., PRL 131 106801 (2023)

[2] Krauth, Moessner, PRB 67 064503 (2003)