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...
Main Authors: | , , , , |
---|---|
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 |
_version_ | 1797750913563099136 |
---|---|
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. |
first_indexed | 2024-03-12T16:39:43Z |
format | Article |
id | doaj.art-a6d27166e42546618400fcea80064e54 |
institution | Directory Open Access Journal |
issn | 1367-2630 |
language | English |
last_indexed | 2024-03-12T16:39:43Z |
publishDate | 2016-01-01 |
publisher | IOP Publishing |
record_format | Article |
series | New Journal of Physics |
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 |
work_keys_str_mv | AT titusneupert nogotheoremforbosoncondensationintopologicallyorderedquantumliquids AT huanhe nogotheoremforbosoncondensationintopologicallyorderedquantumliquids AT curtvonkeyserlingk nogotheoremforbosoncondensationintopologicallyorderedquantumliquids AT germansierra nogotheoremforbosoncondensationintopologicallyorderedquantumliquids AT bandreibernevig nogotheoremforbosoncondensationintopologicallyorderedquantumliquids |