Nogo 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 nogo 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:

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^{[2]}
 Univ. of Zurich, Zurich (Switzerland); Princeton Univ., Princeton, NJ (United States)
 Princeton Univ., Princeton, NJ (United States)
 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 13672630
 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) (SC22)
 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. Nogo theorem for boson condensation in topologically ordered quantum liquids. United States: N. p.,
Web. doi:10.1088/13672630/18/12/123009.
Neupert, Titus, He, Huan, Keyserlingk, Curt von, Sierra, Germán, & Bernevig, B. Andrei. Nogo theorem for boson condensation in topologically ordered quantum liquids. United States. doi:10.1088/13672630/18/12/123009.
Neupert, Titus, He, Huan, Keyserlingk, Curt von, Sierra, Germán, and Bernevig, B. Andrei. 2016.
"Nogo theorem for boson condensation in topologically ordered quantum liquids". United States.
doi:10.1088/13672630/18/12/123009. https://www.osti.gov/servlets/purl/1357776.
@article{osti_1357776,
title = {Nogo 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 nogo 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 = {10.1088/13672630/18/12/123009},
journal = {New Journal of Physics},
number = 12,
volume = 18,
place = {United States},
year = {2016},
month = {12}
}