Student or educator? Sign up with your school email and get 6 months of Pro free.
CoChat
Sign Up
Cited by 368

The DOI matches its Crossref record; 9 of the 9 references it cites were found in a registry or an index.

Machine learning quantum phases of matter beyond the fermion sign problem

Open access
Broecker, Peter, Carrasquilla, Juan, Melko, Roger G., Trebst, Simon·2017·Scientific Reports
DOI 10.1038/s41598-017-09098-0
Open this paper in CoChat — free account

Abstract

State-of-the-art machine learning techniques promise to become a powerful tool in statistical mechanics via their capacity to distinguish different phases of matter in an automated way. Here we demonstrate that convolutional neural networks (CNN) can be optimized for quantum many-fermion systems such that they correctly identify and locate quantum phase transitions in such systems. Using auxiliary-field quantum Monte Carlo (QMC) simulations to sample the many-fermion system, we show that the Green’s function holds sufficient information to allow for the distinction of different fermionic phases via a CNN. We demonstrate that this QMC + machine learning approach works even for systems exhibiting a severe fermion sign problem where conventional approaches to extract information from the Green’s function, e.g. in the form of equal-time correlation functions, fail.

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1038/s41598-017-09098-0

Cites

9 of 9 references verified0 citation errors · 0 not checkable

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Show all 9 references

Research works printed but not linked: 41

  1. Hirsch, J. E., Sugar, R. L., Scalapino, D. J. & Blankenbecler, R. Monte carlo simulations of one-dimensional fermion systems. Phys. Rev. B 26, 5033 (1982). · DOI · Paper page
  2. Chandrasekharan, S. & Wiese, U.-J. Meron-Cluster Solution of Fermion Sign Problems. Phys. Rev. Lett. 83, 3116 (1999). · doi:10.1103/physrevlett.83.3116
  3. Chandrasekharan, S. & Li, A. Fermion bag solutions to some sign problems in four-fermion field theories. Phys. Rev. D 85, 091502 (2012). · doi:10.1103/physrevd.85.091502
  4. Li, Z.-X., Jiang, Y.-F. & Yao, H. Solving the fermion sign problem in quantum Monte Carlo simulations by Majorana representation. Phys. Rev. B 91, 241117 (2015a). · DOI · Paper page
  5. Bravyi, S., DiVincenzo, D., Oliveira, R. & Terhal, B. The complexity of stoquastic local Hamiltonian problems. Quant. Inf. Comp. 8, 0361 (2008).
  6. Kaul, R. K., Melko, R. G. & Sandvik, A. W. Bridging Lattice-Scale Physics and Continuum Field Theory with Quantum Monte Carlo Simulations. Annual Review of Condensed Matter Physics 4, 179 (2013). · DOI
  7. Troyer, M. & Wiese, U.-J. Computational Complexity and Fundamental Limitations to Fermionic Quantum Monte Carlo Simulations. Phys. Rev. Lett. 94, 170201 (2005). · DOI · Paper page
  8. Zaanen, J. et al. Towards a complete theory of high Tc. Nature Phys. 2, 138 (2006). · DOI
  9. Schofield, A. J. Non-Fermi liquids. Contemp. Phys. 40, 95 (1999). · doi:10.1080/001075199181602
  10. Löhneysen, H. V., Rosch, A., Vojta, M. & Wölfle, P. Fermi-liquid instabilities at magnetic quantum phase transitions. Mod. Phys. 79, 1015 (2007). · DOI · Paper page
  11. Landau, D. P. & Binder, K. A Guide to Monte Carlo Simulations in Statistical Physics (Cambridge University Press, 2000).
  12. Wang, L. Discovering phase transitions with unsupervised learning. Phys. Rev. B 94, 195105 (2016). · DOI · Paper page
  13. Schmidhuber, J. Deep learning in neural networks: An overview. Networks 61, 85 (2015).
  14. Nielsen, M. A. Neural Networks and Deep Learning (Determination Press, 2015).
  15. Deng, D.-L., Li, X. & Sarma, S. D. Exact machine learning topological states, arXiv:1609.09060. · arXiv
  16. Tubman, N. M. Measuring quantum entanglement, machine learning and wave function tomography: Bridging theory and experiment with the quantum gas microscope, arXiv:1609.08142. · arXiv
  17. Tanaka, A. & Tomiya, A. Detection of phase transition via convolutional neural network. J. Phys. Soc. Jpn. 86, 063001 (2017). · DOI · Paper page
  18. van Nieuwenburg, E. P., Liu, Y.-H. & Huber, S. D. Learning phase transitions by confusion. Nature Physics 13, 435 (2017). · DOI · Paper page
  19. Liu, J., Qi, Y., Meng, Z. Y. & Fu, L. Self-learning monte carlo method. Phys. Rev. B 95, 041101 (2017). · DOI · Paper page
  20. Huang, L. & Wang, L. Accelerate monte carlo simulations with restricted boltzmann machines. Phys. Rev. B 95, 035105 (2017). · DOI · Paper page
  21. Zhang, Y. & Kim, E.-A. Triangular quantum loop topography for machine learning. Phys. Rev. Lett. 118, 216401 (2017). · DOI · Paper page
  22. Portman, N. & Tamblyn, I. Sampling algorithms for validation of supervised learning models for Ising-like systems. arXiv:1611.05891. · arXiv
  23. Huang, L., Feng Yang, Y. & Wang, L. Recommender engine for continuous time quantum monte carlo methods. Phys. Rev. E 95, 031301 (2017). · doi:10.1103/physreve.95.031301
  24. Ohtsuki, T. & Ohtsuki, T. Deep learning the quantum phase transitions in random electron systems: Applications to three dimensions. J. Phys. Soc. Jpn. 86, 044708 (2017). · DOI
  25. Bény, C. Deep learning and the renormalization group, arXiv:1301.3124. · arXiv
  26. Mehta, P. & Schwab, D. J. An exact mapping between the Variational Renormalization Group and Deep Learning, arXiv:1410.3831. · arXiv
  27. Schoenholz, S. S., Cubuk, E. D., Sussman, D. M., Kaxiras, E. & Liu, A. J. A structural approach to relaxation in glassy liquids. Nat. Phys. 12, 469 (2016). · DOI · Paper page
  28. Torlai, G. & Melko, R. G. Learning thermodynamics with boltzmann machines. Phys. Rev. B 94, 165134 (2016). · DOI · Paper page
  29. Stoudenmire, E. & Schwab, D. J. In Advances in Neural Information Processing Systems 29, edited by Lee, D. D., Sugiyama, M., Luxburg, U. V., Guyon, I. & Garnett, R., pp. 4799–4807 (Curran Associates, Inc., 2016).
  30. Otsuka, Y., Yunoki, S. & Sorella, S. Universal quantum criticality in the metal-insulator transition of two-dimensional interacting dirac electrons. Phys. Rev. X 6, 011029 (2016).
  31. Hirsch, J. E. Discrete hubbard-stratonovich transformation for fermion lattice models. Phys. Rev. B 28, 4059 (1983). · DOI · Paper page
  32. Duchon, E., Loh, Y. L. & Trivedi, N. In Novel Superfluids: Volume 2, edited by Bennemann, K.-H. and Ketterson, J. B., Chap. 17 (Oxford University Press, Oxford, 2014).
  33. Ch’ng, K., Carrasquilla, J., Melko, R. G. & Khatami, E. Machine Learning Phases of Strongly Correlated Fermions, arXiv:1609.02552. · arXiv
  34. Foley, J. D., van Dam, A., Feiner, S. K. & Hughes, J. F. Computer Graphics: Principles and Practice (2nd Ed.) (Addison-Wesley Longman Publishing Co., Inc., Boston, MA, USA, 1990).
  35. Meng, Z. Y., Lang, T. C., Wessel, S., Assaad, F. F. & Muramatsu, A. Quantum spin liquid emerging in two-dimensional correlated Dirac fermions. Nature (London) 464, 847 (2010). · DOI · Paper page
  36. Gross, D. J. & Neveu, A. Dynamical symmetry breaking in asymptotically free field theories. Phys. Rev. D 10, 3235 (1974). · DOI · Paper page
  37. Wang, L., Corboz, P. & Troyer, M. Fermionic quantum critical point of spinless fermions on a honeycomb lattice. New Journal of Physics 16, 103008 (2014). · DOI
  38. Li, Z.-X., Jiang, Y.-F. & Yao, H. Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions. New Journal of Physics 17, 085003 (2015b). · DOI
  39. Motruk, J., Grushin, A. G., de Juan, F. & Pollmann, F. Interaction-driven phases in the half-filled honeycomb lattice: An infinite density matrix renormalization group study. Phys. Rev. B 92, 085147 (2015). · DOI
  40. Capponi, S. & Läuchli, A. M. Phase diagram of interacting spinless fermions on the honeycomb lattice: A comprehensive exact diagonalization study. Phys. Rev. B 92, 085146 (2015). · doi:10.1103/physrevb.92.085146
  41. Broecker, P. & Trebst, S. Entanglement and the fermion sign problem in auxiliary field quantum Monte Carlo simulations. Phys. Rev. B 94, 075144 (2016). · DOI

Cited by

See all 368

Metadata

Authors
Broecker, P., Carrasquilla, J., Melko, R. G., & Trebst, S.
Venue
Scientific Reports
Publisher
Springer Science and Business Media LLC
Published
2017-08-18
Volume
7
Issue
1
Pages
8823-8823
ISSN
2045-2322 (ISSN-L)
DOI
10.1038/s41598-017-09098-0
OpenAlex
W2516533688
Cited by
368
References
9
FWCI
24.01
Type
journal article
Language
en
Open access
gold
Licence

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

How to cite

Cite CoChat for the checks on this page, and the paper for its own findings.

This page
CoChat. (2026). Citation check: Machine learning quantum phases of matter beyond the fermion sign problem. https://app.cochat.ai/papers/10.1038/s41598-017-09098-0
The paper
Broecker, P., Carrasquilla, J., Melko, R. G., & Trebst, S. (2017). Machine learning quantum phases of matter beyond the fermion sign problem. Scientific Reports. https://doi.org/10.1038/s41598-017-09098-0

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.