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

Titus Neupert, Huan He, Curt Von Keyserlingk, Germán Sierra, B. Andrei Bernevig

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10 Scopus citations


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.

Original languageEnglish (US)
Article number123009
JournalNew Journal of Physics
Issue number12
StatePublished - Dec 2016

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


  • Bose-Einstein condensation
  • topological order
  • topological quantum field theory


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