- 2250 Elings Hall
- Q Seminar
Even though 2+1D topological phases are gapped by definition, their non-trivial physics stems from their relation to a gapless theory in one dimension less. The most famous example is the correspondence between fractional quantum Hall phases and (chiral) Conformal Field Theories (CFTs). In this talk, I will show how this correspondence can be generalized to interacting Symmetry Protected Topological (SPTs) states. Starting from various microscopic SPT wavefunctions, the corresponding gapless theory is identified as an auxiliary 2D classical statistical mechanics model for which the weights are given by the wavefunction amplitude (crucially, not squared). These auxiliary models are shown to flow to various (achiral) CFTs, which allows us to rewrite the SPT wavefunction as a correlator in this CFT, to obtain the entanglement spectrum, and to show the existence of ``hidden order'' by using a plasma analogy. Since the symmetry acts in an anomalous way on these statistical mechanics models, they are naturally described in terms of non-local objects, like loops, even when the wavefunction amplitude is given in terms of group cocycles. Finally, I will show that this description provides a simple way of studying critical transitions between different SPT phases.