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Information Center for Mathematical Science

세미나

Information Center for Mathematical Science

세미나

2018 KAIST Physics Seminar
Title Natural compact representation of Matsubara Green’s functions: applications to analytic continuation and quantum many-body simulations"
Date 2018-12-11
Speaker Hiroshi Shinaoka (Saitama University)
Sponsors 2018-12-11
Host KAIST
Place E6-2. 1st fl. #1323
Abstract Sparse modeling is a powerful framework for data analysis and processing such as image denoising and super-resolution. Sparse modeling assumes that a signal to be processed can be efficiently represented by a sparse linear combination of some basis vectors (e.g., wavelets for image). In this talk, we introduce our “sparse-modeling” methods for solving many-body problems. Our framework relies on a recently developed generic compact representation of imaginary-time (Matsubara) Green’s functions [1]. The basis functions of this “intermediate representation” (IR) are defined by the singular value decomposition of the kernel of the Lehmann representation of Green’s functions [1].We show that the data size of any single/two-particle Green’s function increases only logarithmically with inverse temperature [2,3]. We present applications of this natural compact representation. First, we introduce our new method to extract a spectral function from noisy quantum Monte Carlo data (analytic continuation) [4]. Furthermore, we show some unpublished data on efficient quantum many-body simulations accelerated by the use of the IR basis. Open-source softwares for analytic continuation [5] and the IR basis [6] are available online.