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arXiv · 1910.04908

A many-body Fredholm index for ground state spaces and Abelian anyons

Sven Bachmann·Alex Bols·Wojciech De Roeck·Martin Fraas
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Abstract

We propose a many-body index that extends Fredholm index theory to many-body systems. The index is defined for any charge-conserving 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 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 provides an explicit construction of Wilson loop operators exhibiting a non-trivial braiding and that can be used to create fractionally charged Abelian anyons.

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Sven Bachmann, Alex Bols, Wojciech De Roeck, Martin Fraas. 2019-10-10. A many-body Fredholm index for ground state spaces and Abelian anyons. https://doi.org/10.1103/physrevb.101.085138

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