Informal CMT Forum: Pok Man Tam

Quantum Shape of Matter

Geometry has shaped our understanding of the physical world since antiquity. In today’s quantum era, advances in experimental probes are revealing a new notion of “shape” encoded in the wavefunctions of quantum matter.

In this talk, I will show how topology and geometry provide powerful frameworks for characterizing quantum materials and give rise to experimentally accessible signatures. First, I will discuss the topology of metallic systems, where global properties of the Fermi sea define distinct phases, and present recent developments demonstrating how quantized correlation and transport effects can probe this topology in both solid-state and ultracold-atom platforms.

I will then discuss the notion of quantum geometry, which describes the local structure of electronic wavefunctions, and show how charge fluctuations provide a versatile probe of the quantum metric in both insulators and metals. Together, these results illustrate how the “quantum shape” of matter can be directly accessed in experiments and connected to the information content of many-body systems, opening new avenues for understanding and engineering quantum materials.