“Topological Bounds”
Topology is a powerful concept in modern condensed matter physics. It provides a unified framework for understanding quantized physical responses and protected boundary states. In this talk, I will explore broader implications of topology in quantum many-body systems. Specifically, I will show that nontrivial topology imposes universal bounds on both ground- and excited-state properties. Two results will be given: (1) an upper bound on the energy gap of topological Chern insulators characterized by quantized Hall conductivity; (2) a lower bound on the static structure factor at long wavelength. Our results are derived entirely from basic principles of physics and are also intimately connected with (many-body) quantum geometry. Interestingly, these topological bounds are found to be fairly tight for (fractional) Chern insulator states that were recently observed in twisted semiconductor bilayers.
Host: Daniil Antonenko