The Anthony J Leggett Institute for Condensed Matter Special Theory Seminar, Jie Wang (Peking University), "Density Matrix Quantum Geometry and Exact Sum Rules"
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- Physics - The Anthony J Leggett Institute for Condensed Matter Theory Seminar
Abstract: Geometry is a fundamental mathematical concept that also plays a crucial role in characterizing the local properties of quantum states, including both pure and mixed states. Pure-state geometry — often referred to as wavefunction geometry — is known to be important in many areas of zero-temperature condensed matter physics, such as the anomalous Hall effect and electron localization. Mixed-state geometry, or density matrix geometry, is essential in quantum information science, with applications in quantum metrology and entanglement witness. In this talk, I will present our recent work (arXiv:2507.14028) relating the finite-temperature response of a quantum system to the geometries of the thermal density matrix in a general setting. As a specific example, we discuss the application to optical responses and new exact sum rules for orbital magnetization in general interacting systems.