Guo Chuan Thiang, Jingbo Xia
Published 2024-01-15Version 1
We identify the quantized Hall conductance of Landau levels with a Fredholm index, by using the theories of Helton-Howe-Carey-Pincus, and Toeplitz operators on the classic Fock space and higher Fock spaces. The index computations reduce to the single elementary one for the lowest Landau level. This brings new insights to the extraordinarily accurate quantization of the Hall conductance as measured in quantum Hall experiments.
Generic Jumps of Fredholm Indices and the Quantum Hall Effect
Hall conductance and the statistics of flux insertions in gapped interacting lattice systems
Quantization of Hall Conductance For Interacting Electrons Without Averaging Assumptions
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