IAS CMP/QFT Group Meeting

Abstract: We often say two gapped lattice Hamiltonians are in the same topological phase if they are connected by a path of gapped Hamiltonians. For 2D spin systems, it is conjectured that each phase is uniquely specified by the modular tensor category describing the anyon content and the chiral central charge. However, it is unclear how to show that these provide a complete set of invariants. Meanwhile, the tensor category alone is conjectured to uniquely specify the topological phase up to stacking with invertible phases. I describe an argument for the latter conjecture under some simplifying assumptions.