TY - JOUR
T1 - Sparse modeling in quantum many-body problems
AU - Otsuki, Junya
AU - Ohzeki, Masayuki
AU - Shinaoka, Hiroshi
AU - Yoshimi, Kazuyoshi
N1 - Funding Information:
We would like to thank K. Hukushima, Y. Nakanishi-Ohno, H. Tsunetsugu, Y. Motoyama, and N. Chikano for useful comments and discussions. This work was supported by JSPS KAKENHI Grant No. 18H01158. J.O. was supported by JSPS KAKENHI Grant No. 18H04301 (J-Physics). M.O. was supported by MEXT KAKENHI Grant No. 25120008, JST CREST, and JSPS KAKENHI No. 16H04382. H.S. was supported by JSPS KAKENHI Grant Nos. 16H01064 (J-Physics) and 16K17735. K.Y. was supported by JSPS KAKENHI Grant No. 19K03649, and the Building of Consortia for the Development of Human Resources in Science and Technology, MEXT, Japan.
Funding Information:
Junya Otsuki was born in Kyoto, Japan in 1980. He received B.Sc. (2003), M.Sc. (2005), and Ph.D. (2008) degrees from Tohoku University. From 2008 to 2018, he was an assistant professor in the Department of Physics, Tohoku University. From 2011 to 2013, he was at the University of Augsburg as part of a JSPS fellowship. Since 2018, he has been an associate professor in the Research Institute for Interdisciplinary Science, Okayama University. His interests includes magnetism and superconductivity correlated electron systems and development of numerical Masayuki Ohzeki graduated with a Ph.D. in physics from Tokyo Institute of Technology in 2008, and subsequently spent one and a half years as a postdoctoral fellow. He worked as an assistant professor in Kyoto University. Since 2016, he has been an associate professor at the Graduate School of Information Sciences at Tohoku University. He has also been appointed an associate professor at Tokyo Tech and CEO at Sigma-i Co. Ltd. His research interests are broad, including machine learning and its potential both from a perspective of theoretical physics and of itself. He was awarded the 6th Young Scientists’ Award of the Physical Society of Japan, and the Young Scientists’ Prize by The Commendation for Science and Technology by the Minister of Education, Culture, Sports, Science and Technology in 2016.
Funding Information:
Acknowledgments We would like to thank K. Hukushima, Y. Nakanishi-Ohno, H. Tsunetsugu, Y. Motoyama, and N. Chikano for useful comments and discussions. This work was supported by JSPS KAKENHI Grant No. 18H01158. J.O. was supported by JSPS KAKENHI Grant No. 18H04301 (J-Physics). M.O. was supported by MEXT KAKENHI Grant No. 25120008, JST CREST, and JSPS KAKENHI No. 16H04382. H.S. was supported by JSPS KAKENHI Grant Nos. 16H01064 (J-Physics) and 16K17735. K.Y. was supported by JSPS KAKENHI Grant No. 19K03649, and the Building of Consortia for the Development of Human Resources in Science and Technology, MEXT, Japan.
Publisher Copyright:
© 2020 The Physical Society of Japan
PY - 2020
Y1 - 2020
N2 - This review paper describes the basic concept and technical details of sparse modeling and its applications to quantum many-body problems. Sparse modeling refers to methodologies for finding a small number of relevant parameters that well explain a given dataset. This concept reminds us physics, where the goal is to find a small number of physical laws that are hidden behind complicated phenomena. Sparse modeling extends the target of physics from natural phenomena to data, and may be interpreted as “physics for data”. The first half of this review introduces sparse modeling for physicists. It is assumed that readers have physics background but no expertise in data science. The second half reviews applications. Matsubara Green's function, which plays a central role in descriptions of correlated systems, has been found to be sparse, meaning that it contains little information. This leads to (i) a new method for solving the ill-conditioned inverse problem for analytical continuation, and (ii) a highly compact representation of Matsubara Green's function, which enables efficient calculations for quantum many-body systems.
AB - This review paper describes the basic concept and technical details of sparse modeling and its applications to quantum many-body problems. Sparse modeling refers to methodologies for finding a small number of relevant parameters that well explain a given dataset. This concept reminds us physics, where the goal is to find a small number of physical laws that are hidden behind complicated phenomena. Sparse modeling extends the target of physics from natural phenomena to data, and may be interpreted as “physics for data”. The first half of this review introduces sparse modeling for physicists. It is assumed that readers have physics background but no expertise in data science. The second half reviews applications. Matsubara Green's function, which plays a central role in descriptions of correlated systems, has been found to be sparse, meaning that it contains little information. This leads to (i) a new method for solving the ill-conditioned inverse problem for analytical continuation, and (ii) a highly compact representation of Matsubara Green's function, which enables efficient calculations for quantum many-body systems.
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U2 - 10.7566/JPSJ.89.012001
DO - 10.7566/JPSJ.89.012001
M3 - Article
AN - SCOPUS:85078125073
SN - 0031-9015
VL - 89
JO - Journal of the Physical Society of Japan
JF - Journal of the Physical Society of Japan
IS - 1
M1 - 012001
ER -