Condensation and Stability of Topological Order in Tensor Networks

Explore the stability of topological order in tensor networks and its connection to condensation of topological excitations in this 54-minute lecture by Dominic Williamson. Delve into the intriguing contrast between the stability of quantum topological order under Hamiltonian perturbations at zero temperature and the instability of tensor network representations of ground states with topological order in two spatial dimensions. Examine the relationship between topological order stability in tensor networks and the condensation of specific topological excitations determined by local tensor choice. Investigate the argument for the stability of topological order in certain tensor network representations of three-dimensional discrete gauge theories. This talk was presented as part of the Thematic Programme on "Tensor Networks: Mathematical Structures and Novel Algorithms" at the Erwin Schrödinger International Institute for Mathematics and Physics.