CMSA Quantum Matter in Mathematics and Physics: Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers

SEMINARS, CMSA EVENTS

Speaker:

Junkai Dong - Harvard University

The Motivated by the higher Chern bands of twisted graphene multilayers, we consider flat bands with

arbitrary Chern number C with ideal quantum geometry. While C>1 bands differ from Landau levels, we

show that these bands host exact fractional Chern insulator (FCI) ground states for short range

interactions. We show how to decompose ideal higher Chern bands into separate ideal bands with Chern

number 1 that are intertwined through translation and rotation symmetry. The decomposed bands admit

an SU(C) action that combines real space and momentum space translations. Remarkably, they also

allow for analytic construction of exact many-body ground states, such as generalized quantum Hall

ferromagnets and FCIs, including flavor-singlet Halperin states and Laughlin ferromagnets in the limit

of short-range interactions. In this limit, the SU(C) action is promoted to a symmetry on the ground state

subspace. While flavor singlet states are translation symmetric, the flavor ferromagnets correspond to

translation broken states and admit charged skyrmion excitations corresponding to a spatially varying

density wave pattern. We confirm our analytic predictions with numerical simulations of ideal bands of

twisted chiral multilayers of graphene, and discuss consequences for experimentally accessible systems

such as monolayer graphene twisted relative to a Bernal bilayer.

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