Event

Geometry describes how quantum states change locally in parameter space and governs many important physical phenomena, including many-body phases and their responses. The classic example of zero-temperature geometry includes the Berry curvature and quantum metric. At finite temperature, it is natural to consider density matrices rather than wavefunctions, and in fact, the canonical extension of curvature and metric to mixed states was achieved by Uhlmann. The first part of the talk will focus on geometric sum rules, which are valid at any temperature and for any interaction, and their relation to the geometry of thermal density matrices. The second part will discuss using the geometric properties of coherent states to construct exact quantum Hall physics on a lattice, as well as their relevance for ultracold atom platforms. These together argue geometry as an organizing principle for many-body phases and responses.