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Hall conductance and Avron-Dana-Zak relation for interacting systems

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No logo availableBanff International Research Station (BIRS) for Mathematical Innovation and Discovery
 Bols, Alexander

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Hall conductance and Avron-Dana-Zak relation for interacting systems
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The Avron-Dana-Zak relation constrains the allowed values of the Hall conductivity and the charge density in the ground state of a spatially periodic Hall fluid with rational flux per unit cell
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14
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CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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Abstract
As an application of the many-body index (see Sven Bachmann's talk), the Avron-Dana-Zak relation is shown to hold in the context of interacting quantum lattice systems, for the integer and fractional quantum Hall effects. A key formal property used to obtain this result is the additivity of the many-body index.