Department of Physics, Saitama University, Saitama, Japan
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 . 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 .
First, we discuss the properties of the IR basis. A surprising point is that the data size of any single/two-particle Green’s function increases only logarithmically with inverse temperature [2,3]. Then, we introduce our new method to extract a spectral function from noisy quantum Monte Carlo data (analytic continuation) . Open-source soft wares for analytic continuation  and the IR basis  are now available. We may show some unpublished data on efficient quantum chemistry calculations and quantum Monte Carlo measurement of two-particle Green’s functions.
 H. Shinaoka, J. Otsuki, M. Ohzeki, K. Yoshimi, PRB 96, 035147 (2017).
 N. Chikano, J. Otsuki, H. Shinaoka, PRB 98, 035104 (2018).
 H. Shinaoka, J. Otsuki, K. Haule, M. Wallerberger, E. Gull, K. Yoshimi, and M. Ohzeki, PRB 97, 205111 (2018).
 J. Otsuki, M. Ohzeki, H. Shinaoka, K. Yoshimi, PRE 95, 061302(R) (2017).
 N. Chikano, K. Yoshimi, J. Otsuki, H. Shinaoka, arXiv:1807.05237.
Contact: Lei Wang 9853