Quantum Matter Seminar

Gapped phases of two-dimensional free-fermionic systems without any symmetry are classified by an integer-valued topological invariant called the Chern number, which counts the net chirality of boundary modes. It has long been conjectured that systems with distinct Chern numbers cannot be deformed into each other without a phase transition, even in the presence of arbitrarily strong interactions. In this talk, I will present a construction of a quantum many-body index that generalizes the Chern number to the interacting setting and allows us to prove this conjecture. When the edge modes can be described by a conformal field theory, the index provides a microscopic characterization of the chiral central charge.