Many-body Fredholm index for ground-state spaces and Abelian anyons
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Many-body Fredholm index for ground-state spaces and Abelian anyons. / Bachmann, Sven; Bols, Alex; De Roeck, Wojciech; Fraas, Martin.
In: Physical Review B, Vol. 101, No. 8, 085138, 2020.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Many-body Fredholm index for ground-state spaces and Abelian anyons
AU - Bachmann, Sven
AU - Bols, Alex
AU - De Roeck, Wojciech
AU - Fraas, Martin
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85082837473&partnerID=8YFLogxK
U2 - 10.1103/PhysRevB.101.085138
DO - 10.1103/PhysRevB.101.085138
M3 - Journal article
AN - SCOPUS:85082837473
VL - 101
JO - Physical Review B
JF - Physical Review B
SN - 2469-9950
IS - 8
M1 - 085138
ER -
ID: 257976923