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

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

doi:10.1088/1367-2630/18/12/123009

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

Journal Article · Wed Dec 07 00:00:00 EST 2016 · New Journal of Physics

DOI:https://doi.org/10.1088/1367-2630/18/12/123009· OSTI ID:1357776

^[1]; He, Huan ^[2]; Keyserlingk, Curt von ^[2]; Sierra, Germán ^[3]; Bernevig, B. Andrei ^[2]

Univ. of Zurich, Zurich (Switzerland); Princeton Univ., Princeton, NJ (United States)
Princeton Univ., Princeton, NJ (United States)
Instituto de Fisica Teorica, Madrid (Spain)

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.

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Research Organization:: Princeton Univ., Princeton, NJ (United States). Princeton Center for Theoretical Science

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0016239

OSTI ID:: 1357776

Journal Information:: New Journal of Physics, Vol. 18, Issue 12; ISSN 1367-2630

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 8 works

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