Symmetry constraints on low-energy properties of quantum many-body systems

Chang-Tse Hsieh^1,2,3*

¹Department of Physics, National Taiwan University, Taipei, Taiwan
²Physics Division, National Center for Theoretical Science, Taipei, Taiwan
³Center for Theoretical Physics, National Taiwan University, Taipei, Taiwan

* Presenter:Chang-Tse Hsieh, email:cthsieh@phys.ntu.edu.tw

In contemporary condensed matter physics, the spin and orbital degrees of electrons, which can be propagated through matter with varying orientations, play an essential role. However, many of the low-temperature properties in strongly correlated systems, or more generally in quantum many-body systems, cannot be understood based solely on free electrons or single particles. In this talk, I will present a method of constraining the low-energy behaviors of a generic many-body system, based directly on the system's symmetry. These constraints can be verified through direct numerical analysis and are expected to yield experimentally testable predictions. At the heart of this research method is the concept of "quantum anomaly", which was originally introduced in particle physics but has now become crucial in understanding certain phenomena in condensed matter. This highlights the significance of the interplay between these two distinct fields of physics.

Keywords: symmetry, quantum many-body systems, critical phenomena, quantum anomaly, Lieb-Schultz-Mattis theorem