Bionic fractionalization in the trimer model of twisted bilayer graphene

TL;DR

This paper investigates a triangular trimer model inspired by twisted bilayer graphene, revealing complex phases with fractionalized excitations and proposing a new field theory to describe critical phenomena and emergent gauge charges.

Contribution

It introduces a novel field theory for the trimer model, demonstrating fractionalization and fracton physics, and provides extensive Monte Carlo simulations of its phase diagram.

Findings

Identification of a polar fluid and brick-wall phase with fractional charge e/3 excitations.

Derivation of a U(1)×U(1) gauge theory describing the critical trimer liquid phase.

Numerical evidence of algebraic correlations indicating fractionalized gauge charges.

Abstract

Motivated by the rapid experimental progress in twisted van der Waals materials, we study the triangular trimer model as a representative framework for extended Wannier orbitals in twisted bilayer graphene at 1/3-filling. This deceptively simple model exhibits a rich suite of complex phases, including unusual excitations exhibiting the physics of fractionalization and fractons. For our investigations, we carry out extensive Monte Carlo simulations using an efficient cluster algorithm. The so-obtained finite-temperature phase diagram reveals a novel polar fluid and an ordered brick-wall phase characterized by fractionally charged $e/3$ excitations with subdimensional lineonic dynamics. Notably, we identify a critical trimer liquid phase for the particularly simple model of hard trimers. For this, we derive a new field theory which takes the form of a U(1)$\times$U(1) gauge theory. Its $e/3$ monomers are fractionalized bionic excitations: they carry a {\it pair} of emergent gauge charges, as evidenced by algebraic correlations with two distinct exponents. These field theoretical predictions offer theoretical grounds for numerical observations of critical exponents. Our study highlights the triangular trimer model as a new key platform for investigating fractionalization and fractons, where trimer liquid bionic monomers can transform into lineons or fractons in proximate phases, and calls for experimental investigations of this physics in twisted van der Waals materials and a broader class of systems with intermediate-range interactions.