No-go theorem for boson condensation in topologically ordered quantum liquids. (7th December 2016)

• Record Type: Journal Article
• Authors: Neupert, Titus; He, Huan; Keyserlingk, Curt von; Sierra, Germán; Bernevig, B Andrei
• Is Part Of: New journal of physics. Volume 18:Number 12(2016:Dec.)
• Publication Date: 2016-12-07
• Subjects: topological order -- Bose–Einstein condensation -- topological quantum field theory; 03.67.Mn -- 05.30.Pr -- 73.43.-f; Physics -- Periodicals; Physics; Periodicals; 530.05
• DOI: 10.1088/1367-2630/18/12/123009
• Languages: English
• ISSNs: 1367-2630

Abstract

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. This includes (as the case k = 3) the noncondensability of any number of layers of the Fibonacci TQFT.