No-Go Theorem for Boson Condensation in Topologically Ordered Quantum   Liquids
  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. 
Titus Neupert, Huan He, Curt von Keyserlingk, German Sierra, B. Andrei   Bernevig
cond-mat.str-el quant-ph