No-Go Theorem for Boson Condensation in Topologically Ordered Quantum Liquids

Abstract

Certain phase transitions between topological quantum field theories (TQFT) 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.

arXiv comment4 pages, 2 figures plus 3 pages Supplemental Information

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• Anyon condensation and its applications
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• Entanglement Entropy From Tensor Network States for Stabilizer Codes
• Hamiltonian and Algebraic Theories of Gapped Boundaries in Topological Phases of Matter
• Entanglement bootstrap approach for gapped domain walls
• Boundary theory of the X-cube model in the continuum
• Gapped boundaries of (3+1)d topological orders
• Quantum criticality in many-body parafermion chains
• Higher Hall conductivity from a single wave function: Obstructions to symmetry-preserving gapped edge of (2+1)D topological order