DMFT and Quantum Embedding Group Meeting

Monday Oct 5, 2020, 11:00 AM → 12:00 PM America/New_York

Virtual

Speaker: Kun Chen

A representation theory of the thermal Green’s function

We propose a universal theory to construct compact representations of thermal Green's functions in quantum systems. We first give a criterion to measure the quality of Green's function representations. We then use the principal component analysis to optimize the solution. The optimal basis functions are indexed by a compressed real-frequency and their importance exponentially decays. We find that the zero-temperature basis set corresponds to the Mellin transform, while the finite-temperature set is isomorphic to the eigenspace of the Hilbert Matrix. With proper infrared/ultraviolet regularizations, the compressed frequency is automatically discretized and the representation is then particularly useful to compress the Green's functions in numerical simulations (This use case is first proposed in Ref [H. Shinaoka, et.al, Phys. Rev. B 96, 035147 (2017)]).