---
_id: '12150'
abstract:
- lang: eng
  text: Methods inspired from machine learning have recently attracted great interest
    in the computational study of quantum many-particle systems. So far, however,
    it has proven challenging to deal with microscopic models in which the total number
    of particles is not conserved. To address this issue, we propose a variant of
    neural network states, which we term neural coherent states. Taking the Fröhlich
    impurity model as a case study, we show that neural coherent states can learn
    the ground state of nonadditive systems very well. In particular, we recover exact
    diagonalization in all regimes tested and observe substantial improvement over
    the standard coherent state estimates in the most challenging intermediate-coupling
    regime. Our approach is generic and does not assume specific details of the system,
    suggesting wide applications.
acknowledgement: 'We acknowledge fruitful discussions with G. Bighin, G. Fabiani,
  A. Ghazaryan, C. Lampert, and A. Volosniev at various stages of this work. W.R.
  acknowledges support through a DOC Fellowship of the Austrian Academy of Sciences
  and has received funding from the EU Horizon 2020 programme under the Marie Skłodowska-Curie
  Grant Agreement No. 665385. M.L. and J.H.M. acknowledge support by the European
  Research Council (ERC) Starting Grant No. 801770 (ANGULON) and Synergy Grant No.
  856538 (3D-MAGiC), respectively. This work is part of the Shell-NWO/FOMinitiative
  “Computational sciences for energy research” of Shell and Chemical Sciences, Earth
  and Life Sciences, Physical Sciences, FOM and STW. '
article_number: '155127'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Wojciech
  full_name: Rzadkowski, Wojciech
  id: 48C55298-F248-11E8-B48F-1D18A9856A87
  last_name: Rzadkowski
  orcid: 0000-0002-1106-4419
- first_name: Mikhail
  full_name: Lemeshko, Mikhail
  id: 37CB05FA-F248-11E8-B48F-1D18A9856A87
  last_name: Lemeshko
  orcid: 0000-0002-6990-7802
- first_name: Johan H.
  full_name: Mentink, Johan H.
  last_name: Mentink
citation:
  ama: Rzadkowski W, Lemeshko M, Mentink JH. Artificial neural network states for
    nonadditive systems. <i>Physical Review B</i>. 2022;106(15). doi:<a href="https://doi.org/10.1103/physrevb.106.155127">10.1103/physrevb.106.155127</a>
  apa: Rzadkowski, W., Lemeshko, M., &#38; Mentink, J. H. (2022). Artificial neural
    network states for nonadditive systems. <i>Physical Review B</i>. American Physical
    Society. <a href="https://doi.org/10.1103/physrevb.106.155127">https://doi.org/10.1103/physrevb.106.155127</a>
  chicago: Rzadkowski, Wojciech, Mikhail Lemeshko, and Johan H. Mentink. “Artificial
    Neural Network States for Nonadditive Systems.” <i>Physical Review B</i>. American
    Physical Society, 2022. <a href="https://doi.org/10.1103/physrevb.106.155127">https://doi.org/10.1103/physrevb.106.155127</a>.
  ieee: W. Rzadkowski, M. Lemeshko, and J. H. Mentink, “Artificial neural network
    states for nonadditive systems,” <i>Physical Review B</i>, vol. 106, no. 15. American
    Physical Society, 2022.
  ista: Rzadkowski W, Lemeshko M, Mentink JH. 2022. Artificial neural network states
    for nonadditive systems. Physical Review B. 106(15), 155127.
  mla: Rzadkowski, Wojciech, et al. “Artificial Neural Network States for Nonadditive
    Systems.” <i>Physical Review B</i>, vol. 106, no. 15, 155127, American Physical
    Society, 2022, doi:<a href="https://doi.org/10.1103/physrevb.106.155127">10.1103/physrevb.106.155127</a>.
  short: W. Rzadkowski, M. Lemeshko, J.H. Mentink, Physical Review B 106 (2022).
date_created: 2023-01-12T12:07:49Z
date_published: 2022-10-15T00:00:00Z
date_updated: 2023-08-04T09:01:48Z
day: '15'
department:
- _id: MiLe
doi: 10.1103/physrevb.106.155127
ec_funded: 1
external_id:
  arxiv:
  - '2105.15193'
  isi:
  - '000875189100005'
intvolume: '       106'
isi: 1
issue: '15'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: ' https://doi.org/10.48550/arXiv.2105.15193'
month: '10'
oa: 1
oa_version: Preprint
project:
- _id: 05A235A0-7A3F-11EA-A408-12923DDC885E
  grant_number: '25681'
  name: Analytic and machine learning approaches to composite quantum impurities
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '665385'
  name: International IST Doctoral Program
- _id: 2688CF98-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '801770'
  name: 'Angulon: physics and applications of a new quasiparticle'
publication: Physical Review B
publication_identifier:
  eissn:
  - 2469-9969
  issn:
  - 2469-9950
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Artificial neural network states for nonadditive systems
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 106
year: '2022'
...
---
_id: '8644'
abstract:
- lang: eng
  text: Determining the phase diagram of systems consisting of smaller subsystems
    'connected' via a tunable coupling is a challenging task relevant for a variety
    of physical settings. A general question is whether new phases, not present in
    the uncoupled limit, may arise. We use machine learning and a suitable quasidistance
    between different points of the phase diagram to study layered spin models, in
    which the spin variables constituting each of the uncoupled systems (to which
    we refer as layers) are coupled to each other via an interlayer coupling. In such
    systems, in general, composite order parameters involving spins of different layers
    may emerge as a consequence of the interlayer coupling. We focus on the layered
    Ising and Ashkin–Teller models as a paradigmatic case study, determining their
    phase diagram via the application of a machine learning algorithm to the Monte
    Carlo data. Remarkably our technique is able to correctly characterize all the
    system phases also in the case of hidden order parameters, i.e. order parameters
    whose expression in terms of the microscopic configurations would require additional
    preprocessing of the data fed to the algorithm. We correctly retrieve the three
    known phases of the Ashkin–Teller model with ferromagnetic couplings, including
    the phase described by a composite order parameter. For the bilayer and trilayer
    Ising models the phases we find are only the ferromagnetic and the paramagnetic
    ones. Within the approach we introduce, owing to the construction of convolutional
    neural networks, naturally suitable for layered image-like data with arbitrary
    number of layers, no preprocessing of the Monte Carlo data is needed, also with
    regard to its spatial structure. The physical meaning of our results is discussed
    and compared with analytical data, where available. Yet, the method can be used
    without any a priori knowledge of the phases one seeks to find and can be applied
    to other models and structures.
acknowledgement: We thank Gesualdo Delfino, Michele Fabrizio, Piero Ferrarese, Robert
  Konik, Christoph Lampert and Mikhail Lemeshko for stimulating discussions at various
  stages of this work. WR has received funding from the EU Horizon 2020 program under
  the Marie Skłodowska-Curie Grant Agreement No. 665385 and is a recipient of a DOC
  Fellowship of the Austrian Academy of Sciences. GB acknowledges support from the
  Austrian Science Fund (FWF), under project No. M2641-N27. ND acknowledges support
  by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) via Collaborative
  Research Center SFB 1225 (ISOQUANT)--project-id 273811115--and under Germany's Excellence
  Strategy 'EXC-2181/1-390900948' (the Heidelberg STRUCTURES Excellence Cluster).
article_number: '093026'
article_processing_charge: No
article_type: original
author:
- first_name: Wojciech
  full_name: Rzadkowski, Wojciech
  id: 48C55298-F248-11E8-B48F-1D18A9856A87
  last_name: Rzadkowski
  orcid: 0000-0002-1106-4419
- first_name: N
  full_name: Defenu, N
  last_name: Defenu
- first_name: S
  full_name: Chiacchiera, S
  last_name: Chiacchiera
- first_name: A
  full_name: Trombettoni, A
  last_name: Trombettoni
- first_name: Giacomo
  full_name: Bighin, Giacomo
  id: 4CA96FD4-F248-11E8-B48F-1D18A9856A87
  last_name: Bighin
  orcid: 0000-0001-8823-9777
citation:
  ama: Rzadkowski W, Defenu N, Chiacchiera S, Trombettoni A, Bighin G. Detecting composite
    orders in layered models via machine learning. <i>New Journal of Physics</i>.
    2020;22(9). doi:<a href="https://doi.org/10.1088/1367-2630/abae44">10.1088/1367-2630/abae44</a>
  apa: Rzadkowski, W., Defenu, N., Chiacchiera, S., Trombettoni, A., &#38; Bighin,
    G. (2020). Detecting composite orders in layered models via machine learning.
    <i>New Journal of Physics</i>. IOP Publishing. <a href="https://doi.org/10.1088/1367-2630/abae44">https://doi.org/10.1088/1367-2630/abae44</a>
  chicago: Rzadkowski, Wojciech, N Defenu, S Chiacchiera, A Trombettoni, and Giacomo
    Bighin. “Detecting Composite Orders in Layered Models via Machine Learning.” <i>New
    Journal of Physics</i>. IOP Publishing, 2020. <a href="https://doi.org/10.1088/1367-2630/abae44">https://doi.org/10.1088/1367-2630/abae44</a>.
  ieee: W. Rzadkowski, N. Defenu, S. Chiacchiera, A. Trombettoni, and G. Bighin, “Detecting
    composite orders in layered models via machine learning,” <i>New Journal of Physics</i>,
    vol. 22, no. 9. IOP Publishing, 2020.
  ista: Rzadkowski W, Defenu N, Chiacchiera S, Trombettoni A, Bighin G. 2020. Detecting
    composite orders in layered models via machine learning. New Journal of Physics.
    22(9), 093026.
  mla: Rzadkowski, Wojciech, et al. “Detecting Composite Orders in Layered Models
    via Machine Learning.” <i>New Journal of Physics</i>, vol. 22, no. 9, 093026,
    IOP Publishing, 2020, doi:<a href="https://doi.org/10.1088/1367-2630/abae44">10.1088/1367-2630/abae44</a>.
  short: W. Rzadkowski, N. Defenu, S. Chiacchiera, A. Trombettoni, G. Bighin, New
    Journal of Physics 22 (2020).
date_created: 2020-10-11T22:01:14Z
date_published: 2020-09-01T00:00:00Z
date_updated: 2024-08-07T07:16:53Z
day: '01'
ddc:
- '530'
department:
- _id: MiLe
doi: 10.1088/1367-2630/abae44
ec_funded: 1
external_id:
  isi:
  - '000573298000001'
file:
- access_level: open_access
  checksum: c9238fff422e7a957c3a0d559f756b3a
  content_type: application/pdf
  creator: dernst
  date_created: 2020-10-12T12:18:47Z
  date_updated: 2020-10-12T12:18:47Z
  file_id: '8650'
  file_name: 2020_NewJournalPhysics_Rzdkowski.pdf
  file_size: 2725143
  relation: main_file
  success: 1
file_date_updated: 2020-10-12T12:18:47Z
has_accepted_license: '1'
intvolume: '        22'
isi: 1
issue: '9'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '665385'
  name: International IST Doctoral Program
- _id: 05A235A0-7A3F-11EA-A408-12923DDC885E
  grant_number: '25681'
  name: Analytic and machine learning approaches to composite quantum impurities
- _id: 26986C82-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: M02641
  name: A path-integral approach to composite impurities
publication: New Journal of Physics
publication_identifier:
  issn:
  - '13672630'
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
related_material:
  record:
  - id: '10759'
    relation: dissertation_contains
    status: public
scopus_import: '1'
status: public
title: Detecting composite orders in layered models via machine learning
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 22
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...