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

摘要: Certain phase transitions between topological quantum field theories (TQFT) are driven by the condensation of bosonic anyons. However, as bosons in a TQFT themselves nontrivial collective excitations, there can be obstructions that prevent them from condensing. Here we formulate such an obstruction form no-go theorem. We use it to show no is possible SO(3)$_k$ TQFTs with odd $k$. further layered theory obtained tensoring itself any integer number times does not admit either. This includes (as case $k=3$) noncondensability layers Fibonacci TQFT.