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Topological Quantum Computing
Quantum Simulation
A many-body Fredholm index for ground state spaces and Abelian anyons
arXiv
Authors: Sven Bachmann, Alex Bols, Wojciech De Roeck, Martin Fraas
Year
2019
Paper ID
7280
Status
Preprint
Abstract Read
~2 min
Abstract Words
92
Citations
N/A
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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- This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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- We propose a many-body index that extends Fredholm index theory to many-body systems.
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