Many-body Fredholm index for ground-state spaces and Abelian anyons
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- Noise-robust exploration of many-body quantum states on near-term quantum devices
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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 short proof of the quantization of the Hall conductance and of the Lieb-Schulz-Mattis theorem. In the case that the index is not an integer, the argument provides an explicit construction of Wilson loop operators exhibiting a nontrivial braiding that can be used to create fractionally charged Abelian anyons.
Original language | English |
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Article number | 085138 |
Journal | Physical Review B |
Volume | 101 |
Issue number | 8 |
Number of pages | 6 |
ISSN | 2469-9950 |
DOIs | |
Publication status | Published - 2020 |
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ID: 257976923