Identification and characterization of topological order without and with tensor networks

Description

Abstract:
Topological phases exhibit order which cannot be characterized by local order parameters, but rather requires to look at the global entanglement structure and its signatures in the nature of elementary excitations. While this is well understood for RG fixed points, characterizing topological order away from fixed point wavefunctions is much more challenging. In my talk, I will discuss two different ways how to identify and characterize topological order and transitions between topological phases, which can both be understood as different ways to generalize the same kind of order parameter at the RG fixed point. The first construction is a simple and physically measurable order parameter for detecting topological order which can be used in experimental scenarios where knowledge of the exact state is limited. The second construction provides a way to define order parameters directly at the level of the entanglement, where it can probe signatures of global topological entanglement order. Both constructions rely on the formalism of tensor networks, which provide an entanglement-based description of complex many-body wavefunctions: In the first construction, tensor networks form a mathematical tool for proving that the order parameter performs as desired, while in the second construction, the order parameter is constructed directly at the entanglement degrees of freedom of a tensor network description.

Period	15 Nov 2023
Held at	California Institute of Technology (Caltech), United States, California
Degree of Recognition	International