Self-learning Monte Carlo method: Continuous-time algorithm
Abstract
The recently introduced self-learning Monte Carlo method is a general-purpose numerical method that speeds up Monte Carlo simulations by training an effective model to propose uncorrelated configurations in the Markov chain. We implement this method in the framework of a continuous-time Monte Carlo method with an auxiliary field in quantum impurity models. We introduce and train a diagram generating function (DGF) to model the probability distribution of auxiliary field configurations in continuous imaginary time, at all orders of diagrammatic expansion. Furthermore, by using DGF to propose global moves in configuration space, we show that the self-learning continuous-time Monte Carlo method can significantly reduce the computational complexity of the simulation.
- Authors:
-
- Japan Atomic Energy Agency, Chiba (Japan); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Hong Kong Univ. of Science and Technology, Hong Kong (China)
- Publication Date:
- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE
- OSTI Identifier:
- 1505622
- Alternate Identifier(s):
- OSTI ID: 1396308
- Grant/Contract Number:
- SC0010526
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 96; Journal Issue: 16; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING
Citation Formats
Nagai, Yuki, Shen, Huitao, Qi, Yang, Liu, Junwei, and Fu, Liang. Self-learning Monte Carlo method: Continuous-time algorithm. United States: N. p., 2017.
Web. doi:10.1103/physrevb.96.161102.
Nagai, Yuki, Shen, Huitao, Qi, Yang, Liu, Junwei, & Fu, Liang. Self-learning Monte Carlo method: Continuous-time algorithm. United States. https://doi.org/10.1103/physrevb.96.161102
Nagai, Yuki, Shen, Huitao, Qi, Yang, Liu, Junwei, and Fu, Liang. Tue .
"Self-learning Monte Carlo method: Continuous-time algorithm". United States. https://doi.org/10.1103/physrevb.96.161102. https://www.osti.gov/servlets/purl/1505622.
@article{osti_1505622,
title = {Self-learning Monte Carlo method: Continuous-time algorithm},
author = {Nagai, Yuki and Shen, Huitao and Qi, Yang and Liu, Junwei and Fu, Liang},
abstractNote = {The recently introduced self-learning Monte Carlo method is a general-purpose numerical method that speeds up Monte Carlo simulations by training an effective model to propose uncorrelated configurations in the Markov chain. We implement this method in the framework of a continuous-time Monte Carlo method with an auxiliary field in quantum impurity models. We introduce and train a diagram generating function (DGF) to model the probability distribution of auxiliary field configurations in continuous imaginary time, at all orders of diagrammatic expansion. Furthermore, by using DGF to propose global moves in configuration space, we show that the self-learning continuous-time Monte Carlo method can significantly reduce the computational complexity of the simulation.},
doi = {10.1103/physrevb.96.161102},
journal = {Physical Review B},
number = 16,
volume = 96,
place = {United States},
year = {2017},
month = {10}
}
Web of Science
Figures / Tables:

Works referenced in this record:
Momentum-selective metal-insulator transition in the two-dimensional Hubbard model: An 8-site dynamical cluster approximation study
journal, July 2009
- Werner, Philipp; Gull, Emanuel; Parcollet, Olivier
- Physical Review B, Vol. 80, Issue 4
Quantum Entanglement in Neural Network States
journal, May 2017
- Deng, Dong-Ling; Li, Xiaopeng; Das Sarma, S.
- Physical Review X, Vol. 7, Issue 2
Monte Carlo Method for Magnetic Impurities in Metals
journal, June 1986
- Hirsch, J. E.; Fye, R. M.
- Physical Review Letters, Vol. 56, Issue 23
Self-learning Monte Carlo method
journal, January 2017
- Liu, Junwei; Qi, Yang; Meng, Zi Yang
- Physical Review B, Vol. 95, Issue 4
Accelerated Monte Carlo simulations with restricted Boltzmann machines
journal, January 2017
- Huang, Li; Wang, Lei
- Physical Review B, Vol. 95, Issue 3
Low-temperature density matrix renormalization group using regulated polynomial expansion
journal, September 2008
- Sota, Shigetoshi; Tohyama, Takami
- Physical Review B, Vol. 78, Issue 11
Superconductivity from Emerging Magnetic Moments
journal, December 2015
- Hoshino, Shintaro; Werner, Philipp
- Physical Review Letters, Vol. 115, Issue 24
Numerical evaluation of Green's functions based on the Chebyshev expansion
journal, October 2014
- Braun, A.; Schmitteckert, P.
- Physical Review B, Vol. 90, Issue 16
Localized Magnetic States in Metals
journal, October 1961
- Anderson, P. W.
- Physical Review, Vol. 124, Issue 1
Numerical study of the two-dimensional Hubbard model
journal, July 1989
- White, S. R.; Scalapino, D. J.; Sugar, R. L.
- Physical Review B, Vol. 40, Issue 1
Efficient Numerical Approach to Inhomogeneous Superconductivity: The Chebyshev-Bogoliubov–de Gennes Method
journal, October 2010
- Covaci, L.; Peeters, F. M.; Berciu, M.
- Physical Review Letters, Vol. 105, Issue 16
Continuous-time Monte Carlo methods for quantum impurity models
journal, May 2011
- Gull, Emanuel; Millis, Andrew J.; Lichtenstein, Alexander I.
- Reviews of Modern Physics, Vol. 83, Issue 2
Efficient Numerical Self-Consistent Mean-Field Approach for Fermionic Many-Body Systems by Polynomial Expansion on Spectral Density
journal, February 2012
- Nagai, Yuki; Ota, Yukihiro; Machida, Masahiko
- Journal of the Physical Society of Japan, Vol. 81, Issue 2
Self-learning quantum Monte Carlo method in interacting fermion systems
journal, July 2017
- Xu, Xiao Yan; Qi, Yang; Liu, Junwei
- Physical Review B, Vol. 96, Issue 4
Recommender engine for continuous-time quantum Monte Carlo methods
journal, March 2017
- Huang, Li; Yang, Yi-feng; Wang, Lei
- Physical Review E, Vol. 95, Issue 3
Two-dimensional Hubbard model: Numerical simulation study
journal, April 1985
- Hirsch, J. E.
- Physical Review B, Vol. 31, Issue 7
Critical temperature enhancement of topological superconductors: A dynamical mean-field study
journal, June 2016
- Nagai, Yuki; Hoshino, Shintaro; Ota, Yukihiro
- Physical Review B, Vol. 93, Issue 22
Monte Carlo calculations of coupled boson-fermion systems. I
journal, October 1981
- Blankenbecler, R.; Scalapino, D. J.; Sugar, R. L.
- Physical Review D, Vol. 24, Issue 8
Continuous-time auxiliary-field Monte Carlo for quantum impurity models
journal, May 2008
- Gull, E.; Werner, P.; Parcollet, O.
- EPL (Europhysics Letters), Vol. 82, Issue 5
Electronic orders in multiorbital Hubbard models with lifted orbital degeneracy
journal, April 2016
- Hoshino, Shintaro; Werner, Philipp
- Physical Review B, Vol. 93, Issue 15
Continuous-time quantum Monte Carlo method for fermions
journal, July 2005
- Rubtsov, A. N.; Savkin, V. V.; Lichtenstein, A. I.
- Physical Review B, Vol. 72, Issue 3
Self-learning Monte Carlo method and cumulative update in fermion systems
journal, June 2017
- Liu, Junwei; Shen, Huitao; Qi, Yang
- Physical Review B, Vol. 95, Issue 24
Quantum Loop Topography for Machine Learning
journal, May 2017
- Zhang, Yi; Kim, Eun-Ah
- Physical Review Letters, Vol. 118, Issue 21
Detection of Phase Transition via Convolutional Neural Networks
journal, June 2017
- Tanaka, Akinori; Tomiya, Akio
- Journal of the Physical Society of Japan, Vol. 86, Issue 6
Discovering phases, phase transitions, and crossovers through unsupervised machine learning: A critical examination
journal, June 2017
- Hu, Wenjian; Singh, Rajiv R. P.; Scalettar, Richard T.
- Physical Review E, Vol. 95, Issue 6
Learning phase transitions by confusion
journal, February 2017
- van Nieuwenburg, Evert P. L.; Liu, Ye-Hua; Huber, Sebastian D.
- Nature Physics, Vol. 13, Issue 5
Solving the quantum many-body problem with artificial neural networks
journal, February 2017
- Carleo, Giuseppe; Troyer, Matthias
- Science, Vol. 355, Issue 6325
Machine learning phases of matter
journal, February 2017
- Carrasquilla, Juan; Melko, Roger G.
- Nature Physics, Vol. 13, Issue 5
Submatrix updates for the continuous-time auxiliary-field algorithm
journal, February 2011
- Gull, Emanuel; Staar, Peter; Fuchs, Sebastian
- Physical Review B, Vol. 83, Issue 7
Continuous-Time Solver for Quantum Impurity Models
journal, August 2006
- Werner, Philipp; Comanac, Armin; de’ Medici, Luca
- Physical Review Letters, Vol. 97, Issue 7
Chebyshev matrix product state impurity solver for dynamical mean-field theory
journal, September 2014
- Wolf, F. Alexander; McCulloch, Ian P.; Parcollet, Olivier
- Physical Review B, Vol. 90, Issue 11
Continuous-time auxiliary field Monte Carlo for quantum impurity models
text, January 2008
- Gull, Emanuel; Werner, Philipp; Parcollet, Olivier
- arXiv
Sub-matrix updates for the Continuous-Time Auxiliary Field algorithm
text, January 2010
- Gull, Emanuel; Staar, Peter; Fuchs, Sebastian
- arXiv
Efficient Numerical Self-consistent Mean-field Approach for Fermionic Many-body Systems by Polynomial Expansion on Spectral Density
text, January 2011
- Nagai, Yuki; Ota, Yukihiro; Machida, Masahiko
- arXiv
Superconductivity from emerging magnetic moments
text, January 2015
- Hoshino, Shintaro; Werner, Philipp
- arXiv
Detection of phase transition via convolutional neural network
text, January 2016
- Tanaka, Akinori; Tomiya, Akio
- arXiv
Learning phase transitions by confusion
text, January 2016
- van Nieuwenburg, Evert P. L.; Liu, Ye-Hua; Huber, Sebastian D.
- arXiv
Quantum Entanglement in Neural Network States
text, January 2017
- Deng, Dong-Ling; Li, Xiaopeng; Sarma, S. Das
- arXiv
Discovering Phases, Phase Transitions and Crossovers through Unsupervised Machine Learning: A critical examination
text, January 2017
- Hu, Wenjian; Singh, Rajiv R. P.; Scalettar, Richard T.
- arXiv
A continuous-time solver for quantum impurity models
text, January 2005
- Werner, Philipp; Comanac, Armin; De Medici, Luca
- arXiv
Works referencing / citing this record:
Accelerating small-angle scattering experiments on anisotropic samples using kernel density estimation
journal, February 2019
- Saito, Kotaro; Yano, Masao; Hino, Hideitsu
- Scientific Reports, Vol. 9, Issue 1
Itinerant quantum critical point with fermion pockets and hotspots
journal, August 2019
- Liu, Zi Hong; Pan, Gaopei; Xu, Xiao Yan
- Proceedings of the National Academy of Sciences, Vol. 116, Issue 34
Revealing fermionic quantum criticality from new Monte Carlo techniques
journal, August 2019
- Xu, Xiao Yan; Hong Liu, Zi; Pan, Gaopei
- Journal of Physics: Condensed Matter, Vol. 31, Issue 46
Accelerating lattice quantum Monte Carlo simulations using artificial neural networks: Application to the Holstein model
journal, July 2019
- Li, Shaozhi; Dee, Philip M.; Khatami, Ehsan
- Physical Review B, Vol. 100, Issue 2
Restricted Boltzmann machine learning for solving strongly correlated quantum systems
journal, November 2017
- Nomura, Yusuke; Darmawan, Andrew S.; Yamaji, Youhei
- Physical Review B, Vol. 96, Issue 20
Real-space mapping of topological invariants using artificial neural networks
journal, March 2018
- Carvalho, D.; García-Martínez, N. A.; Lado, J. L.
- Physical Review B, Vol. 97, Issue 11
Self-learning Monte Carlo with deep neural networks
journal, May 2018
- Shen, Huitao; Liu, Junwei; Fu, Liang
- Physical Review B, Vol. 97, Issue 20
Symmetry-enforced self-learning Monte Carlo method applied to the Holstein model
journal, July 2018
- Chen, Chuang; Xu, Xiao Yan; Liu, Junwei
- Physical Review B, Vol. 98, Issue 4
Itinerant quantum critical point with frustration and a non-Fermi liquid
journal, July 2018
- Liu, Zi Hong; Xu, Xiao Yan; Qi, Yang
- Physical Review B, Vol. 98, Issue 4
Deep learning topological invariants of band insulators
journal, August 2018
- Sun, Ning; Yi, Jinmin; Zhang, Pengfei
- Physical Review B, Vol. 98, Issue 8
Elective-momentum ultrasize quantum Monte Carlo method
journal, February 2019
- Liu, Zi Hong; Xu, Xiao Yan; Qi, Yang
- Physical Review B, Vol. 99, Issue 8
Flow-based generative models for Markov chain Monte Carlo in lattice field theory
journal, August 2019
- Albergo, M. S.; Kanwar, G.; Shanahan, P. E.
- Physical Review D, Vol. 100, Issue 3
Smallest neural network to learn the Ising criticality
journal, August 2018
- Kim, Dongkyu; Kim, Dong-Hee
- Physical Review E, Vol. 98, Issue 2
Policy-guided Monte Carlo: Reinforcement-learning Markov chain dynamics
journal, December 2018
- Bojesen, Troels Arnfred
- Physical Review E, Vol. 98, Issue 6
Machine Learning Topological Invariants with Neural Networks
journal, February 2018
- Zhang, Pengfei; Shen, Huitao; Zhai, Hui
- Physical Review Letters, Vol. 120, Issue 6
Discriminative Cooperative Networks for Detecting Phase Transitions
journal, April 2018
- Liu, Ye-Hua; van Nieuwenburg, Evert P. L.
- Physical Review Letters, Vol. 120, Issue 17
Charge-Density-Wave Transitions of Dirac Fermions Coupled to Phonons
journal, February 2019
- Chen, Chuang; Xu, Xiao Yan; Meng, Zi Yang
- Physical Review Letters, Vol. 122, Issue 7
Machine learning and the physical sciences
journal, December 2019
- Carleo, Giuseppe; Cirac, Ignacio; Cranmer, Kyle
- Reviews of Modern Physics, Vol. 91, Issue 4
Itinerant quantum critical point with frustration and non-Fermi-liquid
text, January 2017
- Liu, Zi Hong; Xu, Xiao Yan; Qi, Yang
- arXiv
Machine Learning Topological Invariants with Neural Networks
text, January 2017
- Zhang, Pengfei; Shen, Huitao; Zhai, Hui
- arXiv
Self-learning Monte Carlo with Deep Neural Networks
text, January 2018
- Shen, Huitao; Liu, Junwei; Fu, Liang
- arXiv
Real space mapping of topological invariants using artificial neural networks
text, January 2018
- Carvalho, D.; Garcia-Martinez, N. A.; Lado, J. L.
- arXiv
Deep Learning Topological Invariants of Band Insulators
text, January 2018
- Sun, Ning; Yi, Jinmin; Zhang, Pengfei
- arXiv
Flow-based generative models for Markov chain Monte Carlo in lattice field theory
text, January 2019
- Albergo, M. S.; Kanwar, G.; Shanahan, P. E.
- arXiv
Figures / Tables found in this record: