No-go theorem for boson condensation in topologically ordered quantum liquids
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. Furthermore, this includes (as the case k = 3) the noncondensability of any number of layers of the Fibonacci TQFT.
- Authors:
-
[1];
- 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:
- Research Org.:
- Princeton Univ., Princeton, NJ (United States). Princeton Center for Theoretical Science
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1357776
- Grant/Contract Number:
- SC0016239
- Resource 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
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; topological order; Bose–Einstein condensation; topological quantum field theory
Citation Formats
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., 2016.
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. https://doi.org/10.1088/1367-2630/18/12/123009
Neupert, Titus, He, Huan, Keyserlingk, Curt von, Sierra, Germán, and Bernevig, B. Andrei. Wed .
"No-go theorem for boson condensation in topologically ordered quantum liquids". United States. https://doi.org/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 = {Wed Dec 07 00:00:00 EST 2016},
month = {Wed Dec 07 00:00:00 EST 2016}
}
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