Zhenghan Wang: Topology of the space of quantum interactions and anyon models

Speaker
Zhenghan Wang, UC Santa Barbara

Abstract
Given an anyon model B, the space of gapped Hamiltonians that realize this anyon model B is conjectured to be the classifying space of the categorical 2-group Pic(B) of the anyon model B.  We initiate a mathematical formulation of this conjecture based on the space of quantum interactions, and describe the conjectured homotopy and cohomology groups based on quantum error correction code and field theory.