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 [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].

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) [4]. Open-source soft wares for analytic continuation [5] and the IR basis [6] 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 We may show some unpublished data on efficient quantum chemistry calculations and quantum Monte Carlo measurement of two-particle Green’s functions.

[1] H. Shinaoka, J. Otsuki, M. Ohzeki, K. Yoshimi, PRB 96, 035147 (2017).
[2] N. Chikano, J. Otsuki, H. Shinaoka, PRB 98, 035104 (2018).
[3] H. Shinaoka, J. Otsuki, K. Haule, M. Wallerberger, E. Gull, K. Yoshimi, and M. Ohzeki, PRB 97, 205111 (2018).
[4] J. Otsuki, M. Ohzeki, H. Shinaoka, K. Yoshimi, PRE 95, 061302(R) (2017).
[5] https://github.com/SpM-lab/SpM
[6] N. Chikano, K. Yoshimi, J. Otsuki, H. Shinaoka, arXiv:1807.05237.

Contact: Lei Wang 9853