Vortex-Line Condensation in Three Dimensions: A Physical Mechanism for Bosonic Topological Insulators

Bosonic topological insulators (BTIs) in three dimensions are symmetry-protected topological phases protected by time-reversal and boson number conservation symmetries. BTIs in three dimensions were first proposed and classified by the group cohomology theory, which suggests two distinct root states, each carrying a Z(2) index. Soon after, surface anomalous topological orders were proposed to identify different root states of BTIs, which even leads to a new BTI root state beyond the group cohomology classification. In this paper, we propose a universal physical mechanism via vortex-line condensation from a 3D superfluid to achieve all three root states. It naturally produces a bulk topological quantum field theory description for each root state. Topologically ordered states on the surface are rigorously derived by placing topological quantum field theory on an open manifold, which allows us to explicitly demonstrate the bulk-boundary correspondence. Finally, we generalize the mechanism to Z(N) symmetries and discuss potential symmetry-protected topological phases beyond the group cohomology classification.