A perspective on machine learning and data science for strongly correlated electron problems
Abstract
Numerical approaches to the correlated electron problem have achieved considerable success, yet are still constrained by several bottlenecks, including high order polynomial or exponential scaling in system size, long autocorrelation times, challenges in recognizing novel phases, and the Fermion sign problem. Methods in machine learning (ML), artificial intelligence, and data science promise to help address these limitations and open up a new frontier in strongly correlated quantum system simulations. In this paper, we review some of the progress in this area. We begin by examining these approaches in the context of classical models, where their underpinnings and application can be easily illustrated and benchmarked. We then discuss cases where ML methods have enabled scientific discovery. Finally, we will examine their applications in accelerating model solutions in state-of-the-art quantum many-body methods like quantum Monte Carlo and discuss potential future research directions.
- Publication Date:
- Research Org.:
- Univ. of Tennessee, Knoxville, TN (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1897543
- Alternate Identifier(s):
- OSTI ID: 1907641
- Grant/Contract Number:
- SC0022311
- Resource Type:
- Published Article
- Journal Name:
- Carbon Trends
- Additional Journal Information:
- Journal Name: Carbon Trends Journal Volume: 9 Journal Issue: C; Journal ID: ISSN 2667-0569
- Publisher:
- Elsevier
- Country of Publication:
- United Kingdom
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Many-body physics; Quantum materials; Machine learning
Citation Formats
Johnston, Steven, Khatami, Ehsan, and Scalettar, Richard. A perspective on machine learning and data science for strongly correlated electron problems. United Kingdom: N. p., 2022.
Web. doi:10.1016/j.cartre.2022.100231.
Johnston, Steven, Khatami, Ehsan, & Scalettar, Richard. A perspective on machine learning and data science for strongly correlated electron problems. United Kingdom. https://doi.org/10.1016/j.cartre.2022.100231
Johnston, Steven, Khatami, Ehsan, and Scalettar, Richard. Sat .
"A perspective on machine learning and data science for strongly correlated electron problems". United Kingdom. https://doi.org/10.1016/j.cartre.2022.100231.
@article{osti_1897543,
title = {A perspective on machine learning and data science for strongly correlated electron problems},
author = {Johnston, Steven and Khatami, Ehsan and Scalettar, Richard},
abstractNote = {Numerical approaches to the correlated electron problem have achieved considerable success, yet are still constrained by several bottlenecks, including high order polynomial or exponential scaling in system size, long autocorrelation times, challenges in recognizing novel phases, and the Fermion sign problem. Methods in machine learning (ML), artificial intelligence, and data science promise to help address these limitations and open up a new frontier in strongly correlated quantum system simulations. In this paper, we review some of the progress in this area. We begin by examining these approaches in the context of classical models, where their underpinnings and application can be easily illustrated and benchmarked. We then discuss cases where ML methods have enabled scientific discovery. Finally, we will examine their applications in accelerating model solutions in state-of-the-art quantum many-body methods like quantum Monte Carlo and discuss potential future research directions.},
doi = {10.1016/j.cartre.2022.100231},
journal = {Carbon Trends},
number = C,
volume = 9,
place = {United Kingdom},
year = {Sat Oct 01 00:00:00 EDT 2022},
month = {Sat Oct 01 00:00:00 EDT 2022}
}
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1016/j.cartre.2022.100231
https://doi.org/10.1016/j.cartre.2022.100231
Other availability
Search WorldCat to find libraries that may hold this journal
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
New results on Trotter-like approximations
journal, May 1986
- Fye, R. M.
- Physical Review B, Vol. 33, Issue 9
Exact SO(5) Symmetry in the Spin- Fermionic System
journal, October 2003
- Wu, Congjun; Hu, Jiang-ping; Zhang, Shou-cheng
- Physical Review Letters, Vol. 91, Issue 18
Machine learning method for tight-binding Hamiltonian parameterization from ab-initio band structure
journal, January 2021
- Wang, Zifeng; Ye, Shizhuo; Wang, Hao
- npj Computational Materials, Vol. 7, Issue 1
Equivalence of restricted Boltzmann machines and tensor network states
journal, February 2018
- Chen, Jing; Cheng, Song; Xie, Haidong
- Physical Review B, Vol. 97, Issue 8
Maximally localized Wannier functions: Theory and applications
journal, October 2012
- Marzari, Nicola; Mostofi, Arash A.; Yates, Jonathan R.
- Reviews of Modern Physics, Vol. 84, Issue 4
Machine learning quantum phases of matter beyond the fermion sign problem
journal, August 2017
- Broecker, Peter; Carrasquilla, Juan; Melko, Roger G.
- Scientific Reports, Vol. 7, Issue 1
Two-dimensional negative- U Hubbard model
journal, February 1991
- Moreo, A.; Scalapino, D. J.
- Physical Review Letters, Vol. 66, Issue 7
Light Bipolarons Stabilized by Peierls Electron-Phonon Coupling
journal, December 2018
- Sous, John; Chakraborty, Monodeep; Krems, Roman V.
- Physical Review Letters, Vol. 121, Issue 24
The critical temperature of the 2D-Ising model through deep learning autoencoders
journal, December 2020
- Alexandrou, Constantia; Athenodorou, Andreas; Chrysostomou, Charalambos
- The European Physical Journal B, Vol. 93, Issue 12
Langevin simulations of the half-filled cubic Holstein model
journal, October 2020
- Cohen-Stead, B.; Barros, Kipton; Meng, Zy
- Physical Review B, Vol. 102, Issue 16
Machine learning of explicit order parameters: From the Ising model to SU(2) lattice gauge theory
journal, November 2017
- Wetzel, Sebastian J.; Scherzer, Manuel
- Physical Review B, Vol. 96, Issue 18
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
From BCS-like superconductivity to condensation of local pairs: A numerical study of the attractive Hubbard model
journal, July 1996
- Singer, J. M.; Pedersen, M. H.; Schneider, T.
- Physical Review B, Vol. 54, Issue 2
Machine learning vortices at the Kosterlitz-Thouless transition
journal, January 2018
- Beach, Matthew J. S.; Golubeva, Anna; Melko, Roger G.
- Physical Review B, Vol. 97, Issue 4
Two-dimensional attractive Hubbard model and the BCS-BEC crossover
journal, May 2022
- Fontenele, Rodrigo A.; Costa, Natanael C.; dos Santos, Raimundo R.
- Physical Review B, Vol. 105, Issue 18
Orbital structure of the effective pairing interaction in the high-temperature superconducting cuprates
journal, March 2021
- Mai, Peizhi; Balduzzi, Giovanni; Johnston, Steven
- npj Quantum Materials, Vol. 6, Issue 1
Quantum spin liquid emerging in two-dimensional correlated Dirac fermions
journal, April 2010
- Meng, Z. Y.; Lang, T. C.; Wessel, S.
- Nature, Vol. 464, Issue 7290
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
Effective Ruderman–Kittel–Kasuya–Yosida-like Interaction in Diluted Double-exchange Model: Self-learning Monte Carlo Approach
journal, March 2021
- Kohshiro, Hidehiko; Nagai, Yuki
- Journal of the Physical Society of Japan, Vol. 90, Issue 3
Energetics of Domain Walls in the 2D Model
journal, October 1998
- White, Steven R.; Scalapino, D. J.
- Physical Review Letters, Vol. 81, Issue 15
Interplay of Site and Bond Electron-Phonon Coupling in One Dimension
journal, November 2016
- Hohenadler, Martin
- Physical Review Letters, Vol. 117, Issue 20
Theory of the First-Order Magnetic Phase Change in U
journal, January 1966
- Blume, M.
- Physical Review, Vol. 141, Issue 2
Machine learning topological states
journal, November 2017
- Deng, Dong-Ling; Li, Xiaopeng; Das Sarma, S.
- Physical Review B, Vol. 96, Issue 19
Relative importance of nonlinear electron-phonon coupling and vertex corrections in the Holstein model
journal, August 2020
- Dee, Philip M.; Coulter, Jennifer; Kleiner, Kevin G.
- Communications Physics, Vol. 3, Issue 1
Two-dimensional Hubbard model: Numerical simulation study
journal, April 1985
- Hirsch, J. E.
- Physical Review B, Vol. 31, Issue 7
Insulator, metal, or superconductor: The criteria
journal, April 1993
- Scalapino, Douglas J.; White, Steven R.; Zhang, Shoucheng
- Physical Review B, Vol. 47, Issue 13
Smallest neural network to learn the Ising criticality
journal, August 2018
- Kim, Dongkyu; Kim, Dong-Hee
- Physical Review E, Vol. 98, Issue 2
Magnetism and Charge Order in the Honeycomb Lattice
journal, March 2021
- Costa, Natanael C.; Seki, Kazuhiro; Sorella, Sandro
- Physical Review Letters, Vol. 126, Issue 10
Solving the electronic structure problem with machine learning
journal, February 2019
- Chandrasekaran, Anand; Kamal, Deepak; Batra, Rohit
- npj Computational Materials, Vol. 5, Issue 1
Ising‐Model Spin Correlations on the Triangular Lattice
journal, August 1964
- Stephenson, John
- Journal of Mathematical Physics, Vol. 5, Issue 8
Machine learning sparse tight-binding parameters for defects
journal, May 2022
- Schattauer, Christoph; Todorović, Milica; Ghosh, Kunal
- npj Computational Materials, Vol. 8, Issue 1
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
Deriving models for the Kitaev spin-liquid candidate material from first principles
journal, August 2019
- Eichstaedt, Casey; Zhang, Yi; Laurell, Pontus
- Physical Review B, Vol. 100, Issue 7
Bond excitations in the pseudogap phase of the Hubbard model
journal, December 2008
- Macridin, Alexandru; Jarrell, M.
- Physical Review B, Vol. 78, Issue 24
Superconductivity and charge density wave order in the two-dimensional Holstein model
journal, June 2021
- Bradley, Owen; Batrouni, George G.; Scalettar, Richard T.
- Physical Review B, Vol. 103, Issue 23
Introduction to quantum Monte Carlo simulations for fermionic systems
journal, January 2003
- Santos, Raimundo R. dos
- Brazilian Journal of Physics, Vol. 33, Issue 1
Stripe order in the underdoped region of the two-dimensional Hubbard model
journal, November 2017
- Zheng, Bo-Xiao; Chung, Chia-Min; Corboz, Philippe
- Science, Vol. 358, Issue 6367
Competition of pairing and Peierls – charge-density-wave correlations in a two-dimensional electron-phonon model
journal, July 1989
- Scalettar, R. T.; Bickers, N. E.; Scalapino, D. J.
- Physical Review B, Vol. 40, Issue 1
Solving the quantum many-body problem with artificial neural networks
journal, February 2017
- Carleo, Giuseppe; Troyer, Matthias
- Science, Vol. 355, Issue 6325
Extraction of interaction parameters for
α − RuCl 3
journal, June 2022
- Samarakoon, Anjana M.; Laurell, Pontus; Balz, Christian
- Physical Review Research, Vol. 4, Issue 2
Monte Carlo sampling methods using Markov chains and their applications
journal, April 1970
- Hastings, W. K.
- Biometrika, Vol. 57, Issue 1
Density Matrix Renormalization Group Study of the Striped Phase in the 2D Model
journal, February 1998
- White, Steven R.; Scalapino, D. J.
- Physical Review Letters, Vol. 80, Issue 6
Relationship between d-Dimensional Quantal Spin Systems and (d+1)-Dimensional Ising Systems: Equivalence, Critical Exponents and Systematic Approximants of the Partition Function and Spin Correlations
journal, November 1976
- Suzuki, M.
- Progress of Theoretical Physics, Vol. 56, Issue 5
Strong Coupling Superconductivity, Pseudogap, and Mott Transition
journal, May 2012
- Sordi, G.; Sémon, P.; Haule, K.
- Physical Review Letters, Vol. 108, Issue 21
Neural Decoder for Topological Codes
journal, July 2017
- Torlai, Giacomo; Melko, Roger G.
- Physical Review Letters, Vol. 119, Issue 3
Easing the Monte Carlo sign problem
journal, August 2020
- Hangleiter, Dominik; Roth, Ingo; Nagaj, Daniel
- Science Advances, Vol. 6, Issue 33
Plaquette versus ordinary -wave pairing in the -Hubbard model on a width-4 cylinder
journal, July 2020
- Chung, Chia-Min; Qin, Mingpu; Zhang, Shiwei
- Physical Review B, Vol. 102, Issue 4
Discrete Hubbard-Stratonovich transformation for fermion lattice models
journal, October 1983
- Hirsch, J. E.
- Physical Review B, Vol. 28, Issue 7
Sign-Problem-Free Quantum Monte Carlo of the Onset of Antiferromagnetism in Metals
journal, December 2012
- Berg, E.; Metlitski, M. A.; Sachdev, S.
- Science, Vol. 338, Issue 6114
Machine learning in electronic-quantum-matter imaging experiments
journal, June 2019
- Zhang, Yi; Mesaros, A.; Fujita, K.
- Nature, Vol. 570, Issue 7762
Self-learning Monte Carlo method
journal, January 2017
- Liu, Junwei; Qi, Yang; Meng, Zi Yang
- Physical Review B, Vol. 95, Issue 4
On the possibility of first-order phase transitions in Ising systems of triplet ions with zero-field splitting
journal, May 1966
- Capel, H. W.
- Physica, Vol. 32, Issue 5
Interplay of charge, spin, and lattice degrees of freedom in the spectral properties of the one-dimensional Hubbard-Holstein model
journal, November 2014
- Nocera, A.; Soltanieh-ha, M.; Perroni, C. A.
- Physical Review B, Vol. 90, Issue 19
Physics-informed machine learning
journal, May 2021
- Karniadakis, George Em; Kevrekidis, Ioannis G.; Lu, Lu
- Nature Reviews Physics, Vol. 3, Issue 6
Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications
journal, March 2019
- Li, Zi-Xiang; Yao, Hong
- Annual Review of Condensed Matter Physics, Vol. 10, Issue 1
Monte Carlo tests of renormalization-group predictions for critical phenomena in Ising models
journal, April 2001
- Binder, Kurt; Luijten, Erik
- Physics Reports, Vol. 344, Issue 4-6
Quantum critical points and the sign problem
journal, January 2022
- Mondaini, R.; Tarat, S.; Scalettar, R. T.
- Science, Vol. 375, Issue 6579
Marshall-positiveSU ( N )
journal, February 2015
- Kaul, Ribhu K.
- Physical Review B, Vol. 91, Issue 5
Dynamical mean field theory of polarons and bipolarons in the half-filled Holstein model
journal, July 2006
- Capone, M.; Carta, P.; Ciuchi, S.
- Physical Review B, Vol. 74, Issue 4
Sufficient condition for absence of the sign problem in the fermionic quantum Monte Carlo algorithm
journal, April 2005
- Wu, Congjun; Zhang, Shou-Cheng
- Physical Review B, Vol. 71, Issue 15
Computational Complexity and Fundamental Limitations to Fermionic Quantum Monte Carlo Simulations
journal, May 2005
- Troyer, Matthias; Wiese, Uwe-Jens
- Physical Review Letters, Vol. 94, Issue 17
Scaling theory of Ising spin glasses
journal, June 1984
- McMillan, W. L.
- Journal of Physics C: Solid State Physics, Vol. 17, Issue 18
Classical spin dynamics based on
SU ( N )
journal, September 2021
- Zhang, Hao; Batista, Cristian D.
- Physical Review B, Vol. 104, Issue 10
Machine learning the Hubbard U parameter in DFT+U using Bayesian optimization
journal, November 2020
- Yu, Maituo; Yang, Shuyang; Wu, Chunzhi
- npj Computational Materials, Vol. 6, Issue 1
Superconductivity, charge density waves, and bipolarons in the Holstein model
journal, June 2021
- Nosarzewski, B.; Huang, E. W.; Dee, Philip M.
- Physical Review B, Vol. 103, Issue 23
Intertwined spin, charge, and pair correlations in the two-dimensional Hubbard model in the thermodynamic limit
journal, February 2022
- Mai, Peizhi; Karakuzu, Seher; Balduzzi, Giovanni
- Proceedings of the National Academy of Sciences, Vol. 119, Issue 7
Study of the superconducting order parameter in the two-dimensional negative-
U
journal, August 2018
- Karakuzu, Seher; Seki, Kazuhiro; Sorella, Sandro
- Physical Review B, Vol. 98, Issue 7
Machine-learning-assisted insight into spin ice Dy2Ti2O7
journal, February 2020
- Samarakoon, Anjana M.; Barros, Kipton; Li, Ying Wai
- Nature Communications, Vol. 11, Issue 1
Efficient Dynamical Mean Field Simulation of the Holstein-Hubbard Model
journal, October 2007
- Werner, Philipp; Millis, Andrew J.
- Physical Review Letters, Vol. 99, Issue 14
Unsupervised machine learning account of magnetic transitions in the Hubbard model
journal, January 2018
- Ch'ng, Kelvin; Vazquez, Nick; Khatami, Ehsan
- Physical Review E, Vol. 97, Issue 1
Hubbard model on the honeycomb lattice: From static and dynamical mean-field theories to lattice quantum Monte Carlo simulations
journal, March 2020
- Raczkowski, Marcin; Peters, Robert; Phùng, Thị Thu
- Physical Review B, Vol. 101, Issue 12
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
Extended Dynamical Mean Field Theory Study of the Periodic Anderson Model
journal, July 2003
- Sun, Ping; Kotliar, Gabriel
- Physical Review Letters, Vol. 91, Issue 3
Machine learning on neutron and x-ray scattering and spectroscopies
journal, September 2021
- Chen, Zhantao; Andrejevic, Nina; Drucker, Nathan C.
- Chemical Physics Reviews, Vol. 2, Issue 3
Geometric integration of classical spin dynamics via a mean-field Schrödinger equation
journal, August 2022
- Dahlbom, David; Zhang, Hao; Miles, Cole
- Physical Review B, Vol. 106, Issue 5
Robustness of antiferromagnetism in the Su-Schrieffer-Heeger Hubbard model
journal, August 2022
- Cai, Xun; Li, Zi-Xiang; Yao, Hong
- Physical Review B, Vol. 106, Issue 8
Critical and multicritical behavior in a triangular-lattice-gas Ising model: Repulsive nearest-neighbor and attractive next-nearest-neighbor coupling
journal, May 1983
- Landau, D. P.
- Physical Review B, Vol. 27, Issue 9
Competition between Antiferromagnetic Order and Spin-Liquid Behavior in the Two-Dimensional Periodic Anderson Model at Half Filling
journal, March 1995
- Vekić, M.; Cannon, J. W.; Scalapino, D. J.
- Physical Review Letters, Vol. 74, Issue 12
Quantum Monte Carlo study of lattice polarons in the two-dimensional three-orbital Su–Schrieffer–Heeger model
journal, June 2020
- Li, Shaozhi; Johnston, Steven
- npj Quantum Materials, Vol. 5, Issue 1
Collective Monte Carlo Updating for Spin Systems
journal, January 1989
- Wolff, Ulli
- Physical Review Letters, Vol. 62, Issue 4
Majorana-Time-Reversal Symmetries: A Fundamental Principle for Sign-Problem-Free Quantum Monte Carlo Simulations
journal, December 2016
- Li, Zi-Xiang; Jiang, Yi-Fan; Yao, Hong
- Physical Review Letters, Vol. 117, Issue 26
Ergodicity at large couplings with the determinant Monte Carlo algorithm
journal, November 1991
- Scalettar, Richard T.; Noack, Reinhard M.; Singh, Rajiv R. P.
- Physical Review B, Vol. 44, Issue 19
Meron-Cluster Solution of Fermion Sign Problems
journal, October 1999
- Chandrasekharan, Shailesh; Wiese, Uwe-Jens
- Physical Review Letters, Vol. 83, Issue 16
Determinant quantum Monte Carlo study of the two-dimensional single-band Hubbard-Holstein model
journal, June 2013
- Johnston, S.; Nowadnick, E. A.; Kung, Y. F.
- Physical Review B, Vol. 87, Issue 23
Machine learning of frustrated classical spin models (II): Kernel principal component analysis
journal, June 2018
- Wang, Ce; Zhai, Hui
- Frontiers of Physics, Vol. 13, Issue 5
Ground-state and finite-temperature signatures of quantum phase transitions in the half-filled Hubbard model on a honeycomb lattice
journal, August 2005
- Paiva, Thereza; Scalettar, R. T.; Zheng, W.
- Physical Review B, Vol. 72, Issue 8
Solutions to sign problems in lattice Yukawa models
journal, July 2012
- Chandrasekharan, Shailesh
- Physical Review D, Vol. 86, Issue 2
Systematic Study of -Wave Superconductivity in the 2D Repulsive Hubbard Model
journal, November 2005
- Maier, T. A.; Jarrell, M.; Schulthess, T. C.
- Physical Review Letters, Vol. 95, Issue 23
Anomalously strong near-neighbor attraction in doped 1D cuprate chains
journal, September 2021
- Chen, Zhuoyu; Wang, Yao; Rebec, Slavko N.
- Science, Vol. 373, Issue 6560
Temperature-filling phase diagram of the two-dimensional Holstein model in the thermodynamic limit by self-consistent Migdal approximation
journal, January 2019
- Dee, P. M.; Nakatsukasa, K.; Wang, Y.
- Physical Review B, Vol. 99, Issue 2
Ground-state phase diagram of the t-t ′ -J model
journal, October 2021
- Jiang, Shengtao; Scalapino, Douglas J.; White, Steven R.
- Proceedings of the National Academy of Sciences, Vol. 118, Issue 44
Metallicity in the half-filled Holstein-Hubbard model
journal, November 2008
- Fehske, H.; Hager, G.; Jeckelmann, E.
- EPL (Europhysics Letters), Vol. 84, Issue 5
Pairing fluctuations and pseudogaps in the attractive Hubbard model
journal, July 2001
- Kyung, B.; Allen, S.; Tremblay, A. -M. S.
- Physical Review B, Vol. 64, Issue 7
Classifying snapshots of the doped Hubbard model with machine learning
journal, July 2019
- Bohrdt, Annabelle; Chiu, Christie S.; Ji, Geoffrey
- Nature Physics, Vol. 15, Issue 9
Lattice field theory as a percolation process
journal, April 1988
- Wolff, Ulli
- Physical Review Letters, Vol. 60, Issue 15
Self-learning Monte Carlo method: Continuous-time algorithm
journal, October 2017
- Nagai, Yuki; Shen, Huitao; Qi, Yang
- Physical Review B, Vol. 96, Issue 16
Sign problem in the numerical simulation of many-electron systems
journal, May 1990
- Loh, E. Y.; Gubernatis, J. E.; Scalettar, R. T.
- Physical Review B, Vol. 41, Issue 13
Strange metallicity in the doped Hubbard model
journal, November 2019
- Huang, Edwin W.; Sheppard, Ryan; Moritz, Brian
- Science, Vol. 366, Issue 6468
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
Quantum magnetic properties of the Hubbard model in the square lattice: A quantum Monte Carlo study
journal, September 2013
- Cai, Zi; Hung, Hsiang-Hsuan; Wang, Lei
- Physical Review B, Vol. 88, Issue 12
Three-band Hubbard model: A Monte Carlo study
journal, May 1990
- Dopf, G.; Muramatsu, A.; Hanke, W.
- Physical Review B, Vol. 41, Issue 13
Finite-size effects in Luther-Emery phases of Holstein and Hubbard models
journal, December 2015
- Greitemann, J.; Hesselmann, S.; Wessel, S.
- Physical Review B, Vol. 92, Issue 24
Quantum cluster theories
journal, October 2005
- Maier, Thomas; Jarrell, Mark; Pruschke, Thomas
- Reviews of Modern Physics, Vol. 77, Issue 3
Periodic Anderson model in infinite dimensions
journal, March 1993
- Jarrell, M.; Akhlaghpour, Hossein; Pruschke, Th.
- Physical Review Letters, Vol. 70, Issue 11
Phase diagram of the Hubbard model: Beyond the dynamical mean field
journal, November 2001
- Jarrell, M.; Maier, Th; Hettler, M. H.
- Europhysics Letters (EPL), Vol. 56, Issue 4
Solvable Model of a Spin-Glass
journal, December 1975
- Sherrington, David; Kirkpatrick, Scott
- Physical Review Letters, Vol. 35, Issue 26
Quantum Entanglement in Deep Learning Architectures
journal, February 2019
- Levine, Yoav; Sharir, Or; Cohen, Nadav
- Physical Review Letters, Vol. 122, Issue 6
Machine learning of frustrated classical spin models. I. Principal component analysis
journal, October 2017
- Wang, Ce; Zhai, Hui
- Physical Review B, Vol. 96, Issue 14
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
Discovering phase transitions with unsupervised learning
journal, November 2016
- Wang, Lei
- Physical Review B, Vol. 94, Issue 19
Identifying topological order through unsupervised machine learning
journal, May 2019
- Rodriguez-Nieva, Joaquin F.; Scheurer, Mathias S.
- Nature Physics, Vol. 15, Issue 8
Learning Efficient, Collective Monte Carlo Moves with Variational Autoencoders
journal, May 2022
- Monroe, Jacob I.; Shen, Vincent K.
- Journal of Chemical Theory and Computation, Vol. 18, Issue 6
Visualizing strange metallic correlations in the two-dimensional Fermi-Hubbard model with artificial intelligence
journal, September 2020
- Khatami, Ehsan; Guardado-Sanchez, Elmer; Spar, Benjamin M.
- Physical Review A, Vol. 102, Issue 3
Nonuniversal critical dynamics in Monte Carlo simulations
journal, January 1987
- Swendsen, Robert H.; Wang, Jian-Sheng
- Physical Review Letters, Vol. 58, Issue 2
Sharp Transition for Single Polarons in the One-Dimensional Su-Schrieffer-Heeger Model
journal, December 2010
- Marchand, D. J. J.; De Filippis, G.; Cataudella, V.
- Physical Review Letters, Vol. 105, Issue 26
Monte Carlo Simulation in Statistical Physics
journal, January 1993
- Binder, K.; Heermann, D.; Roelofs, Lyle
- Computers in Physics, Vol. 7, Issue 2
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
Critical temperature for the two-dimensional attractive Hubbard model
journal, May 2004
- Paiva, Thereza; dos Santos, Raimundo R.; Scalettar, R. T.
- Physical Review B, Vol. 69, Issue 18
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
Mitigating the Sign Problem through Basis Rotations
journal, May 2021
- Levy, Ryan; Clark, Bryan K.
- Physical Review Letters, Vol. 126, Issue 21
Split Orthogonal Group: A Guiding Principle for Sign-Problem-Free Fermionic Simulations
journal, December 2015
- Wang, Lei; Liu, Ye-Hua; Iazzi, Mauro
- Physical Review Letters, Vol. 115, Issue 25
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
Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
journal, December 2012
- Sorella, Sandro; Otsuka, Yuichi; Yunoki, Seiji
- Scientific Reports, Vol. 2, Issue 1
Competition among various charge-inhomogeneous states and d -wave superconducting state in Hubbard models on square lattices
journal, January 2018
- Ido, Kota; Ohgoe, Takahiro; Imada, Masatoshi
- Physical Review B, Vol. 97, Issue 4
Fermion bag approach to lattice field theories
journal, July 2010
- Chandrasekharan, Shailesh
- Physical Review D, Vol. 82, Issue 2
Solution to sign problems in half-filled spin-polarized electronic systems
journal, March 2014
- Huffman, Emilie Fulton; Chandrasekharan, Shailesh
- Physical Review B, Vol. 89, Issue 11
Machine learning phases of matter
journal, February 2017
- Carrasquilla, Juan; Melko, Roger G.
- Nature Physics, Vol. 13, Issue 5
Self-learning Monte Carlo with deep neural networks
journal, May 2018
- Shen, Huitao; Liu, Junwei; Fu, Liang
- Physical Review B, Vol. 97, Issue 20
On the product of semi-groups of operators
journal, April 1959
- Trotter, H. F.
- Proceedings of the American Mathematical Society, Vol. 10, Issue 4
Quantum Monte Carlo and exact diagonalization study of a dynamic Hubbard model
journal, May 2002
- Hirsch, J. E.
- Physical Review B, Vol. 65, Issue 21
Generalization of the Fortuin-Kasteleyn-Swendsen-Wang representation and Monte Carlo algorithm
journal, September 1988
- Edwards, Robert G.; Sokal, Alan D.
- Physical Review D, Vol. 38, Issue 6
Principal component analysis for fermionic critical points
journal, November 2017
- Costa, Natanael C.; Hu, Wenjian; Bai, Z. J.
- Physical Review B, Vol. 96, Issue 19
Solving the fermion sign problem in quantum Monte Carlo simulations by Majorana representation
journal, June 2015
- Li, Zi-Xiang; Jiang, Yi-Fan; Yao, Hong
- Physical Review B, Vol. 91, Issue 24
Stripe order from the perspective of the Hubbard model
journal, April 2018
- Huang, Edwin W.; Mendl, Christian B.; Jiang, Hong-Chen
- npj Quantum Materials, Vol. 3, Issue 1
Unsupervised learning of phase transitions: From principal component analysis to variational autoencoders
journal, August 2017
- Wetzel, Sebastian J.
- Physical Review E, Vol. 96, Issue 2
Zero-temperature phases of the two-dimensional Hubbard-Holstein model: A non-Gaussian exact diagonalization study
journal, November 2020
- Wang, Yao; Esterlis, Ilya; Shi, Tao
- Physical Review Research, Vol. 2, Issue 4
Particle-hole asymmetry in the dynamical spin and charge responses of corner-shared 1D cuprates
journal, September 2021
- Li, Shaozhi; Nocera, Alberto; Kumar, Umesh
- Communications Physics, Vol. 4, Issue 1
Breakdown of the Migdal-Eliashberg theory: A determinant quantum Monte Carlo study
journal, April 2018
- Esterlis, I.; Nosarzewski, B.; Huang, E. W.
- Physical Review B, Vol. 97, Issue 14
Stripes on a 6-Leg Hubbard Ladder
journal, September 2003
- White, Steven R.; Scalapino, D. J.
- Physical Review Letters, Vol. 91, Issue 13
Alleviating the sign problem in quantum Monte Carlo simulations of spin-orbit-coupled multiorbital Hubbard models
journal, January 2020
- Kim, Aaram J.; Werner, Philipp; Valentí, Roser
- Physical Review B, Vol. 101, Issue 4
Semi-Metal-Insulator Transition of the Hubbard Model in the Honeycomb Lattice
journal, August 1992
- Sorella, S.; Tosatti, E.
- Europhysics Letters (EPL), Vol. 19, Issue 8
Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
journal, February 1944
- Onsager, Lars
- Physical Review, Vol. 65, Issue 3-4
Observation of spatial charge and spin correlations in the 2D Fermi-Hubbard model
journal, September 2016
- Cheuk, L. W.; Nichols, M. A.; Lawrence, K. R.
- Science, Vol. 353, Issue 6305
Spin density waves in the Hubbard model: A DMFT approach
journal, April 2014
- Peters, Robert; Kawakami, Norio
- Physical Review B, Vol. 89, Issue 15
Sign problem in Monte Carlo simulations of frustrated quantum spin systems
journal, July 2000
- Henelius, Patrik; Sandvik, Anders W.
- Physical Review B, Vol. 62, Issue 2
Bad metallic transport in a cold atom Fermi-Hubbard system
journal, December 2018
- Brown, Peter T.; Mitra, Debayan; Guardado-Sanchez, Elmer
- Science, Vol. 363, Issue 6425
Bypassing the Kohn-Sham equations with machine learning
journal, October 2017
- Brockherde, Felix; Vogt, Leslie; Li, Li
- Nature Communications, Vol. 8, Issue 1
Numerical evidence of fluctuating stripes in the normal state of high- T c cuprate superconductors
journal, November 2017
- Huang, Edwin W.; Mendl, Christian B.; Liu, Shenxiu
- Science, Vol. 358, Issue 6367
Weak-coupling continuous-time quantum Monte Carlo study of the single impurity and periodic Anderson models with -wave superconducting baths
journal, January 2010
- Luitz, David J.; Assaad, Fakher F.
- Physical Review B, Vol. 81, Issue 2
Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension
journal, July 1968
- Lieb, Elliott H.; Wu, F. Y.
- Physical Review Letters, Vol. 21, Issue 3
Cluster Dynamical Mean Field Theory of the Mott Transition
journal, October 2008
- Park, H.; Haule, K.; Kotliar, G.
- Physical Review Letters, Vol. 101, Issue 18
Majorana Positivity and the Fermion Sign Problem of Quantum Monte Carlo Simulations
journal, June 2016
- Wei, Z. C.; Wu, Congjun; Li, Yi
- Physical Review Letters, Vol. 116, Issue 25
Superconductivity and the Pseudogap in the Two-Dimensional Hubbard Model
journal, May 2013
- Gull, Emanuel; Parcollet, Olivier; Millis, Andrew J.
- Physical Review Letters, Vol. 110, Issue 21
Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions
journal, January 1996
- Georges, Antoine; Kotliar, Gabriel; Krauth, Werner
- Reviews of Modern Physics, Vol. 68, Issue 1
Learning thermodynamics with Boltzmann machines
journal, October 2016
- Torlai, Giacomo; Melko, Roger G.
- Physical Review B, Vol. 94, Issue 16
Ising Model for the Transition and Phase Separation in - Mixtures
journal, September 1971
- Blume, M.; Emery, V. J.; Griffiths, Robert B.
- Physical Review A, Vol. 4, Issue 3
Ising models of quantum frustration
journal, May 2001
- Moessner, R.; Sondhi, S. L.
- Physical Review B, Vol. 63, Issue 22
Variational autoencoder analysis of Ising model statistical distributions and phase transitions
journal, March 2022
- Yevick, David
- The European Physical Journal B, Vol. 95, Issue 3
Electron correlations in narrow energy bands
journal, November 1963
- Hubbard, J.
- Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 276, Issue 1365, p. 238-257
Learning quantum phase transitions through topological data analysis
journal, December 2021
- Tirelli, Andrea; Costa, Natanael C.
- Physical Review B, Vol. 104, Issue 23
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
Valence-bond solid to antiferromagnet transition in the two-dimensional Su-Schrieffer-Heeger model by Langevin dynamics
journal, February 2022
- Götz, A.; Beyl, S.; Hohenadler, M.
- Physical Review B, Vol. 105, Issue 8
Quantum Loop Topography for Machine Learning
journal, May 2017
- Zhang, Yi; Kim, Eun-Ah
- Physical Review Letters, Vol. 118, Issue 21
Characterizing the three-orbital Hubbard model with determinant quantum Monte Carlo
journal, April 2016
- Kung, Y. F.; Chen, C. -C.; Wang, Yao
- Physical Review B, Vol. 93, Issue 15
Roadmap on Machine Learning in Electronic Structure
journal, February 2022
- Kulik, Heather; Hammerschmidt, Thomas; Schmidt, Jonathan
- Electronic Structure
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
Quantum Monte Carlo Simulations of the 2D Su-Schrieffer-Heeger Model
journal, January 2021
- Xing, Bo; Chiu, Wei-Ting; Poletti, Dario
- Physical Review Letters, Vol. 126, Issue 1
Similarities between the Hubbard and Periodic Anderson Models at Finite Temperatures
journal, July 2000
- Held, K.; Huscroft, C.; Scalettar, R. T.
- Physical Review Letters, Vol. 85, Issue 2
Excitation spectra and correlation functions of quantum Su-Schrieffer-Heeger models
journal, June 2015
- Weber, Manuel; Assaad, Fakher F.; Hohenadler, Martin
- Physical Review B, Vol. 91, Issue 24
Topological origin of the fermion sign problem
journal, March 2016
- Iazzi, Mauro; Soluyanov, Alexey A.; Troyer, Matthias
- Physical Review B, Vol. 93, Issue 11
Critical Behavior of an Ising Spin-Glass
journal, July 1986
- Singh, Rajiv R. P.; Chakravarty, Sudip
- Physical Review Letters, Vol. 57, Issue 2
Charge order and antiferromagnetism in the extended Hubbard model
journal, June 2019
- Paki, Joseph; Terletska, Hanna; Iskakov, Sergei
- Physical Review B, Vol. 99, Issue 24
Fast and scalable quantum Monte Carlo simulations of electron-phonon models
journal, June 2022
- Cohen-Stead, Benjamin; Bradley, Owen; Miles, Cole
- Physical Review E, Vol. 105, Issue 6