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 suc...

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Main Authors: Titus Neupert, Huan He, Curt von Keyserlingk, Germán Sierra, B Andrei Bernevig
Format: Article
Language:English
Published: IOP Publishing 2016-01-01
Series:New Journal of Physics
Subjects:
Online Access:https://doi.org/10.1088/1367-2630/18/12/123009
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author Titus Neupert
Huan He
Curt von Keyserlingk
Germán Sierra
B Andrei Bernevig
author_facet Titus Neupert
Huan He
Curt von Keyserlingk
Germán Sierra
B Andrei Bernevig
author_sort Titus Neupert
collection DOAJ
description 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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spelling doaj.art-a6d27166e42546618400fcea80064e542023-08-08T14:34:38ZengIOP PublishingNew Journal of Physics1367-26302016-01-01181212300910.1088/1367-2630/18/12/123009No-go theorem for boson condensation in topologically ordered quantum liquidsTitus Neupert0https://orcid.org/0000-0003-0604-041XHuan He1Curt von Keyserlingk2Germán Sierra3B Andrei Bernevig4Department of Physics, University of Zurich , Winterthurerstrasse 190, 8057 Zurich, Switzerland; Princeton Center for Theoretical Science, Princeton University , Princeton, NJ 08544, USADepartment of Physics, Princeton University , Princeton, NJ 08544, USAPrinceton Center for Theoretical Science, Princeton University , Princeton, NJ 08544, USAInstituto de Física Teórica, UAM-CSIC, Madrid, SpainDepartment of Physics, Princeton University , Princeton, NJ 08544, USACertain 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.https://doi.org/10.1088/1367-2630/18/12/123009topological orderBose–Einstein condensationtopological quantum field theory03.67.Mn05.30.Pr73.43.-f
spellingShingle Titus Neupert
Huan He
Curt von Keyserlingk
Germán Sierra
B Andrei Bernevig
No-go theorem for boson condensation in topologically ordered quantum liquids
New Journal of Physics
topological order
Bose–Einstein condensation
topological quantum field theory
03.67.Mn
05.30.Pr
73.43.-f
title No-go theorem for boson condensation in topologically ordered quantum liquids
title_full No-go theorem for boson condensation in topologically ordered quantum liquids
title_fullStr No-go theorem for boson condensation in topologically ordered quantum liquids
title_full_unstemmed No-go theorem for boson condensation in topologically ordered quantum liquids
title_short No-go theorem for boson condensation in topologically ordered quantum liquids
title_sort no go theorem for boson condensation in topologically ordered quantum liquids
topic topological order
Bose–Einstein condensation
topological quantum field theory
03.67.Mn
05.30.Pr
73.43.-f
url https://doi.org/10.1088/1367-2630/18/12/123009
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