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On the deformation quantization of symplectic orbispaces
In the first part of this article we provide a geometrically oriented
approach to the theory of orbispaces which originally had been introduced by
Chen. We explain the notion of a vector orbibundle and characterize the good
sections of a reduced vector orbibundle as the smooth stratified sections. In
the second part of the article we elaborate on the quantizability of a
symplectic orbispace. By adapting Fedosov's method to the orbispace setting we
show that every symplectic orbispace has a deformation quantization. As a
byproduct we obtain that every symplectic orbifold possesses a star product
Charge order and Mott insulating ground states in small-angle twisted bilayer graphene
In this work, we determine states of electronic order of small-angle twisted
bilayer graphene. Ground states are determined for weak and strong couplings
which are representatives for varying distances of the twist-angle from its
magic value. In the weak-coupling regime, charge density waves emerge which
break translational and -rotational symmetry. In the strong
coupling-regime, we find rotational and translational symmetry breaking Mott
insulating states for all commensurate moir\'e band fillings. Depending on the
local occupation of superlattice sites hosting up to four electrons, global
spin-(ferromagnetic) and valley symmetries are also broken which may give rise
to a reduced Landau level degeneracy as observed in experiments for
commensurate band fillings. The formation of those particular electron orders
is traced back to the important role of characteristic non-local interactions
which connect all localized states belonging to one hexagon formed by the AB-
and BA-stacked regions of the superlattice
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