Yugo Onishi

Topology is a key concept in modern condensed matter physics. The existence of the energy gap between the ground state and the excited states allows us to define the topological phases of matter. One of the most remarkable consequences of topology is the universally quantized response, such as (fractional) quantum Hall conductance. In this talk, I will show a new universal feature of topological phases: topological bound. We show a fundamental bound on the structure factor and the energy gap in topological phases characterized by the many-body Chern number. The bound relies only on fundamental physical principles -- causality and non-negativity of energy dissipation -- and thus applies to a wide range of systems with U(1) symmetry, including fractional quantum Hall systems and spin conserved systems such as topological superconductor and chiral spin liquid. Our topological bound reveals new universal information about topological phases of matter.