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

TL;DR

This paper establishes a no-go theorem demonstrating the topological obstructions preventing boson condensation in certain topologically ordered quantum liquids, specifically in SO(3)$_k$ TQFTs with odd $k$ and their layered tensor products.

Contribution

The authors formulate a no-go theorem that identifies topological obstructions to boson condensation in specific TQFTs, extending understanding of phase transitions in topologically ordered systems.

Findings

No condensation in SO(3)$_k$ TQFTs with odd $k$

Layered SO(3)$_k$ TQFTs do not admit condensation transitions

Noncondensability of layers of Fibonacci TQFT

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.