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

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. Furthermore, this includes (as the case k = 3) the noncondensability of any number of layers of the Fibonacci TQFT.
Authors:
ORCiD logo [1] ;  [2] ;  [2] ;  [3] ;  [2]
  1. Univ. of Zurich, Zurich (Switzerland); Princeton Univ., Princeton, NJ (United States)
  2. Princeton Univ., Princeton, NJ (United States)
  3. Instituto de Fisica Teorica, Madrid (Spain)
Publication Date:
Grant/Contract Number:
SC0016239
Type:
Accepted Manuscript
Journal Name:
New Journal of Physics
Additional Journal Information:
Journal Volume: 18; Journal Issue: 12; Journal ID: ISSN 1367-2630
Publisher:
IOP Publishing
Research Org:
Princeton Univ., Princeton, NJ (United States). Princeton Center for Theoretical Science
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; topological order; Bose–Einstein condensation; topological quantum field theory
OSTI Identifier:
1357776

Neupert, Titus, He, Huan, Keyserlingk, Curt von, Sierra, Germán, and Bernevig, B. Andrei. No-go theorem for boson condensation in topologically ordered quantum liquids. United States: N. p., Web. doi:10.1088/1367-2630/18/12/123009.
Neupert, Titus, He, Huan, Keyserlingk, Curt von, Sierra, Germán, & Bernevig, B. Andrei. No-go theorem for boson condensation in topologically ordered quantum liquids. United States. doi:10.1088/1367-2630/18/12/123009.
Neupert, Titus, He, Huan, Keyserlingk, Curt von, Sierra, Germán, and Bernevig, B. Andrei. 2016. "No-go theorem for boson condensation in topologically ordered quantum liquids". United States. doi:10.1088/1367-2630/18/12/123009. https://www.osti.gov/servlets/purl/1357776.
@article{osti_1357776,
title = {No-go theorem for boson condensation in topologically ordered quantum liquids},
author = {Neupert, Titus and He, Huan and Keyserlingk, Curt von and Sierra, Germán and Bernevig, B. Andrei},
abstractNote = {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. Furthermore, this includes (as the case k = 3) the noncondensability of any number of layers of the Fibonacci TQFT.},
doi = {10.1088/1367-2630/18/12/123009},
journal = {New Journal of Physics},
number = 12,
volume = 18,
place = {United States},
year = {2016},
month = {12}
}