A many-body Fredholm index for ground state spaces and Abelian anyons
A many-body Fredholm index for ground state spaces and Abelian anyons
We propose a many-body index that extends Fredholm index theory to many-body systems. The index is defined for any charge-conserving听system with a topologically ordered p-dimensional ground state sector. The index is fractional with the denominator given by p. In particular, this yields a听new short proof of the quantization of the Hall conductance and of Lieb-Schulz-Mattis theorem. In the case that the index is non-integer, the argument听provides an explicit construction of Wilson loop operators exhibiting a non-trivial braiding and that can be used to create fractionally charged Abelian听anyons. This is joint work with S. Bachmann, A. Bols, and W. De Roeck.听
After introducing the problem, its motivation and history, the presentation听will cover the results in听.
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