Agenda

Résumé : Geometrical frustration is a simple yet profound concept in condensed matter physics that can give rise to exotic quantum matters like spin liquid. In this talk, I will study a new source of geometrical frustration from the orbitals instead of the spins of the electrons. A concrete platform for realizing such orbital geometrical frustration is the twisted bilayer graphene (TBG) at fractional filling, where we can map the configurations of electrons to the tiling patterns of trimers. This deceptively simple model of trimers exhibits a rich suite of complex phases, including unusual excitations exhibiting the physics of fractionalization and fractons. I will discuss both the effect of thermal and quantum fluctuations. The 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. Its e/3 monomers are fractionalized bionic excitations: they carry a 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. By mapping the basis of the constrained Hilbert space to tiling patterns, we find an emergent exact global symmetry for the effective quantum model, dubbed « tile-invariant symmetry”. Quantum fluctuation prefers to spontaneously break the tile-invariant symmetry, giving rise to an exotic Mott insulator, with a gapless spectrum. Our study highlights the triangular trimer model as a new key platform for investigating fractionalization and emergent symmetry and calls for experimental investigations of this physics in twisted van der Waals materials and a broader class of systems with intermediate-range interactions.
Refs: DM, et al. Phys. Rev. Lett. 131, 106801 Tian, H., Codecido, E., DM, et al. Dominant 1/3-filling correlated insulator states and orbital geometric frustration in twisted bilayer graphene. Nat. Phys. 20, 1407–1412 (2024). Zhang.K, DM, et al. https://arxiv.org/abs/2410.00092