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No-go theorem for boson condensation in topologically ordered quantum liquids


Neupert, Titus; He, Huan; Keyserlingk, Curt von; Sierra, Germán; Bernevig, B Andrei (2016). No-go theorem for boson condensation in topologically ordered quantum liquids. New Journal of Physics, 18(12):123009.

Abstract

Certain phase transitions between topological quantum field theories (TQFTs) are driven by the condensation of bosonic anyons. However, as bosons in a TQFT are themselves nontrivial collective excitations, there can be topological obstructions that prevent them from condensing. Here we formulate such an obstruction in the form of a no-go theorem. We use it to show that no condensation is possible in SO(3) k TQFTs with odd k. We further show that a 'layered' theory obtained by tensoring SO(3) k TQFT with itself any integer number of times does not admit condensation transitions either. This includes (as the case k = 3) the noncondensability of any number of layers of the Fibonacci TQFT.

Abstract

Certain phase transitions between topological quantum field theories (TQFTs) are driven by the condensation of bosonic anyons. However, as bosons in a TQFT are themselves nontrivial collective excitations, there can be topological obstructions that prevent them from condensing. Here we formulate such an obstruction in the form of a no-go theorem. We use it to show that no condensation is possible in SO(3) k TQFTs with odd k. We further show that a 'layered' theory obtained by tensoring SO(3) k TQFT with itself any integer number of times does not admit condensation transitions either. This includes (as the case k = 3) the noncondensability of any number of layers of the Fibonacci TQFT.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Physics Institute
Dewey Decimal Classification:530 Physics
Language:English
Date:2016
Deposited On:09 Jan 2017 09:35
Last Modified:09 Jan 2017 09:35
Publisher:IOP Publishing
ISSN:1367-2630
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1088/1367-2630/18/12/123009

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