Crystalline invariants of fractional Chern insulators
arxiv(2024)
摘要
In the presence of crystalline symmetry, topologically ordered states can
acquire a host of symmetry-protected invariants. These determine the patterns
of crystalline symmetry fractionalization of the anyons in addition to
fractionally quantized responses to lattice defects. Here we show how ground
state expectation values of partial rotations centered at high symmetry points
can be used to extract crystalline invariants. Using methods from conformal
field theory and G-crossed braided tensor categories, we develop a theory of
invariants obtained from partial rotations, which apply to both Abelian and
non-Abelian topological orders. We then perform numerical Monte Carlo
calculations for projected parton wave functions of fractional Chern
insulators, demonstrating remarkable agreement between theory and numerics. For
the topological orders we consider, we show that the Hall conductivity, filling
fraction, and partial rotation invariants fully characterize the crystalline
invariants of the system. Our results also yield invariants of continuum
fractional quantum Hall states protected by spatial rotational symmetry.
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