TiSe 2 is a band insulator created by lattice fluctuations, not an excitonic insulator
TiSe 2 is a narrow-gap insulator with a rich array of unique properties. In addition to being a superconductor under certain modifications, it is commonly thought to be a rare realisation of an excitonic insulator. Below 200 K, TiSe 2 undergoes a transition from a high-symmetry ($P\bar{3}m1$) phase to a low-symmetry ($P\bar{3}c1$) charge density wave (CDW). Here we establish that it is indeed an insulator in both $P\bar{3}m1$ and $P\bar{3}c1$ phases. However, the insulating state is driven not by excitonic effects but by symmetry-breaking. In the CDW phase it is static. At high temperature, thermally driven instantaneous deviations from $P\bar{3}m1$ break the symmetry on the characteristic time scale of a phonon. Even though the time-averaged lattice structure assumes $P\bar{3}m1$ symmetry, the time-averaged energy band structure is closer to the CDW phase - a rare instance of a metal-insulator transition induced by dynamical symmetry breaking. We establish these conclusions from quasiparticle self-consistent GW (QSGW) and many-body calculations (QS$G\widehat{W}$), in combination with molecular dynamics simulations to capture the effects of thermal disorder. The many-body theory includes explicitly ladder diagrams in the polarizability, which incorporates excitonic effects in an ab initio manner. We find that the excitonic modification to the potential is weak, ruling out the possibility that TiSe 2 is an excitonic insulator.