In the past few years many new symmetry protected topological phases (SPTs) of spin systems have been discovered theoretically. In this talk I'll propose a method for analyzing groundstate wavefunctions of such SPTs using a correspondence with conformal field theories (CFTs) and integrable lattice models.
This method generalizes the CFT approach to the fractional quantum Hall effect wherein the wavefunction amplitude is written as a many-operator correlator in the CFT. Taking a hands-on microscopic approach, I'll start from various known wavefunctions of SPTs and show how the CFT description emerges at large scale. These findings point to an intriguing correspondence between group-cohomology cocycles and critical, often integrable, 2D lattice models. They also allow us to derive several new results concerning hidden order in these wavefunctions and their entanglement spectrum. Time permits, I'll also discuss how new microscopic models for SPTs could be obtained from integrable lattice models. | 
