Abstract:
A central theme in modern condensed matter physics is that the collective behavior of many interacting particles can be far richer than what one might infer from single-particle physics alone. In particular, strongly correlated systems often exhibit emergent phenomena governed not by microscopic details, but by more general physical principles. In this talk, I will discuss how symmetry provides a powerful way to constrain the possible low-energy behavior of quantum many-body systems. A classic example is the Lieb-Schultz-Mattis theorem, which shows that certain one-dimensional quantum magnets cannot have a unique gapped ground state if they preserve spin-rotation and lattice-translation symmetries. I will then present recent generalizations of this idea to a broader class of quantum spin systems, illustrating how symmetry can reveal robust features of quantum matter without requiring the full solution of a complicated many-body problem.