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arXiv · 1607.06457

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

Titus Neupert·Huan He·Curt von Keyserlingk·German Sierra·B. Andrei Bernevig
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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.

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Titus Neupert, Huan He, Curt von Keyserlingk, German Sierra, B. Andrei Bernevig. 2016-07-21. No-Go Theorem for Boson Condensation in Topologically Ordered Quantum Liquids. https://doi.org/10.1088/1367-2630/18/12/123009

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