2026年1月20日（火）13:15~ (13:15-, January 20, 2026)

理学部1号館206教室 (Room No. 206, Science 1st Bldg.) 

Speaker: Yugo Onishi (MIT)
Title: Bound on energy gap in quantum many-body systems 

Abstract:

Quantum many-body systems host a wide range of ground states, from conventional band insulators to topological phases such as integer and fractional quantum Hall states. Some of these ground states possess unique intrinsic properties such as topology, which are encoded directly in the ground-state wavefunction. Another important property is the energy gap, which belongs to the excitation spectrum rather than the ground state itself. The energy gap is the minimum excitation energy and sets the temperature scale at which we can observe ground-state phenomena, such as quantized Hall conductance.

In this talk, I will present how the quantum ground states impose fundamental restriction on the energy gap. I will begin with a simple observation that optical responses always exhibit non-negative energy absorption, and derive a universal relationship between the energy gap and the dielectric constant [1]. I will then show that similar considerations lead to topological bounds on the energy gap in Chern insulators [2]. The resulting bound can be understood through the static structure factor and its relation to the energy gap [3]. These bounds apply to strongly correlated systems, such as fractional quantum Hall systems, offering a useful tool for understanding strongly correlated quantum systems.

References: 

[1] Y. Onishi and L. Fu, Universal Relation between Energy Gap and Dielectric Constant, Phys. Rev. B 110, 155107 (2024).

[2] Y. Onishi and L. Fu, Fundamental Bound on Topological Gap, Phys. Rev. X 14, 011052 (2024).

[3] Y. Onishi and L. Fu, Topological Bound on the Structure Factor, Phys. Rev. Lett. 133, 206602 (2024).