---
_id: '13277'
abstract:
- lang: eng
  text: Recent experimental advances have inspired the development of theoretical
    tools to describe the non-equilibrium dynamics of quantum systems. Among them
    an exact representation of quantum spin systems in terms of classical stochastic
    processes has been proposed. Here we provide first steps towards the extension
    of this stochastic approach to bosonic systems by considering the one-dimensional
    quantum quartic oscillator. We show how to exactly parameterize the time evolution
    of this prototypical model via the dynamics of a set of classical variables. We
    interpret these variables as stochastic processes, which allows us to propose
    a novel way to numerically simulate the time evolution of the system. We benchmark
    our findings by considering analytically solvable limits and providing alternative
    derivations of known results.
acknowledgement: 'S. De Nicola acknowledges funding from the Institute of Science
  and Technology Austria (ISTA), and from the European Union’s Horizon 2020 research
  and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 754411.
  S. De Nicola also acknowledges funding from the EPSRC Center for Doctoral Training
  in Cross-Disciplinary Approaches to NonEquilibrium Systems (CANES) under Grant EP/L015854/1. '
article_number: '029'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Gennaro
  full_name: Tucci, Gennaro
  last_name: Tucci
- first_name: Stefano
  full_name: De Nicola, Stefano
  id: 42832B76-F248-11E8-B48F-1D18A9856A87
  last_name: De Nicola
  orcid: 0000-0002-4842-6671
- first_name: Sascha
  full_name: Wald, Sascha
  last_name: Wald
- first_name: Andrea
  full_name: Gambassi, Andrea
  last_name: Gambassi
citation:
  ama: Tucci G, De Nicola S, Wald S, Gambassi A. Stochastic representation of the
    quantum quartic oscillator. <i>SciPost Physics Core</i>. 2023;6(2). doi:<a href="https://doi.org/10.21468/scipostphyscore.6.2.029">10.21468/scipostphyscore.6.2.029</a>
  apa: Tucci, G., De Nicola, S., Wald, S., &#38; Gambassi, A. (2023). Stochastic representation
    of the quantum quartic oscillator. <i>SciPost Physics Core</i>. SciPost Foundation.
    <a href="https://doi.org/10.21468/scipostphyscore.6.2.029">https://doi.org/10.21468/scipostphyscore.6.2.029</a>
  chicago: Tucci, Gennaro, Stefano De Nicola, Sascha Wald, and Andrea Gambassi. “Stochastic
    Representation of the Quantum Quartic Oscillator.” <i>SciPost Physics Core</i>.
    SciPost Foundation, 2023. <a href="https://doi.org/10.21468/scipostphyscore.6.2.029">https://doi.org/10.21468/scipostphyscore.6.2.029</a>.
  ieee: G. Tucci, S. De Nicola, S. Wald, and A. Gambassi, “Stochastic representation
    of the quantum quartic oscillator,” <i>SciPost Physics Core</i>, vol. 6, no. 2.
    SciPost Foundation, 2023.
  ista: Tucci G, De Nicola S, Wald S, Gambassi A. 2023. Stochastic representation
    of the quantum quartic oscillator. SciPost Physics Core. 6(2), 029.
  mla: Tucci, Gennaro, et al. “Stochastic Representation of the Quantum Quartic Oscillator.”
    <i>SciPost Physics Core</i>, vol. 6, no. 2, 029, SciPost Foundation, 2023, doi:<a
    href="https://doi.org/10.21468/scipostphyscore.6.2.029">10.21468/scipostphyscore.6.2.029</a>.
  short: G. Tucci, S. De Nicola, S. Wald, A. Gambassi, SciPost Physics Core 6 (2023).
date_created: 2023-07-24T10:47:46Z
date_published: 2023-04-14T00:00:00Z
date_updated: 2023-07-31T09:03:28Z
day: '14'
ddc:
- '530'
department:
- _id: MaSe
doi: 10.21468/scipostphyscore.6.2.029
ec_funded: 1
external_id:
  arxiv:
  - '2211.01923'
file:
- access_level: open_access
  checksum: b472bc82108747eda5d52adf9e2ac7f3
  content_type: application/pdf
  creator: dernst
  date_created: 2023-07-31T09:02:27Z
  date_updated: 2023-07-31T09:02:27Z
  file_id: '13329'
  file_name: 2023_SciPostPhysCore_Tucci.pdf
  file_size: 523236
  relation: main_file
  success: 1
file_date_updated: 2023-07-31T09:02:27Z
has_accepted_license: '1'
intvolume: '         6'
issue: '2'
keyword:
- Statistical and Nonlinear Physics
- Atomic and Molecular Physics
- and Optics
- Nuclear and High Energy Physics
- Condensed Matter Physics
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: SciPost Physics Core
publication_identifier:
  issn:
  - 2666-9366
publication_status: published
publisher: SciPost Foundation
quality_controlled: '1'
status: public
title: Stochastic representation of the quantum quartic oscillator
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 6
year: '2023'
...
---
_id: '11337'
abstract:
- lang: eng
  text: 'Nonanalytic points in the return probability of a quantum state as a function
    of time, known as dynamical quantum phase transitions (DQPTs), have received great
    attention in recent years, but the understanding of their mechanism is still incomplete.
    In our recent work [Phys. Rev. Lett. 126, 040602 (2021)], we demonstrated that
    one-dimensional DQPTs can be produced by two distinct mechanisms, namely semiclassical
    precession and entanglement generation, leading to the definition of precession
    (pDQPTs) and entanglement (eDQPTs) dynamical quantum phase transitions. In this
    manuscript, we extend and investigate the notion of p- and eDQPTs in two-dimensional
    systems by considering semi-infinite ladders of varying width. For square lattices,
    we find that pDQPTs and eDQPTs persist and are characterized by similar phenomenology
    as in 1D: pDQPTs are associated with a magnetization sign change and a wide entanglement
    gap, while eDQPTs correspond to suppressed local observables and avoided crossings
    in the entanglement spectrum. However, DQPTs show higher sensitivity to the ladder
    width and other details, challenging the extrapolation to the thermodynamic limit
    especially for eDQPTs. Moving to honeycomb lattices, we also demonstrate that
    lattices with an odd number of nearest neighbors give rise to phenomenologies
    beyond the one-dimensional classification.'
acknowledgement: "We acknowledge support by the European Research Council (ERC) under
  the European Union’s Horizon 2020 research and innovation programme (Grant Agreement
  No. 850899).\r\nS.D.N. also acknowledges funding from the Institute of Science and
  Technology (IST) Austria, and from the European Union’s Horizon 2020 Research and
  Innovation Programme under the Marie Skłodowska-Curie Grant Agreement No. 754411."
article_number: '165149'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Stefano
  full_name: De Nicola, Stefano
  id: 42832B76-F248-11E8-B48F-1D18A9856A87
  last_name: De Nicola
  orcid: 0000-0002-4842-6671
- first_name: Alexios
  full_name: Michailidis, Alexios
  id: 36EBAD38-F248-11E8-B48F-1D18A9856A87
  last_name: Michailidis
- first_name: Maksym
  full_name: Serbyn, Maksym
  id: 47809E7E-F248-11E8-B48F-1D18A9856A87
  last_name: Serbyn
  orcid: 0000-0002-2399-5827
citation:
  ama: De Nicola S, Michailidis A, Serbyn M. Entanglement and precession in two-dimensional
    dynamical quantum phase transitions. <i>Physical Review B</i>. 2022;105. doi:<a
    href="https://doi.org/10.1103/PhysRevB.105.165149">10.1103/PhysRevB.105.165149</a>
  apa: De Nicola, S., Michailidis, A., &#38; Serbyn, M. (2022). Entanglement and precession
    in two-dimensional dynamical quantum phase transitions. <i>Physical Review B</i>.
    American Physical Society. <a href="https://doi.org/10.1103/PhysRevB.105.165149">https://doi.org/10.1103/PhysRevB.105.165149</a>
  chicago: De Nicola, Stefano, Alexios Michailidis, and Maksym Serbyn. “Entanglement
    and Precession in Two-Dimensional Dynamical Quantum Phase Transitions.” <i>Physical
    Review B</i>. American Physical Society, 2022. <a href="https://doi.org/10.1103/PhysRevB.105.165149">https://doi.org/10.1103/PhysRevB.105.165149</a>.
  ieee: S. De Nicola, A. Michailidis, and M. Serbyn, “Entanglement and precession
    in two-dimensional dynamical quantum phase transitions,” <i>Physical Review B</i>,
    vol. 105. American Physical Society, 2022.
  ista: De Nicola S, Michailidis A, Serbyn M. 2022. Entanglement and precession in
    two-dimensional dynamical quantum phase transitions. Physical Review B. 105, 165149.
  mla: De Nicola, Stefano, et al. “Entanglement and Precession in Two-Dimensional
    Dynamical Quantum Phase Transitions.” <i>Physical Review B</i>, vol. 105, 165149,
    American Physical Society, 2022, doi:<a href="https://doi.org/10.1103/PhysRevB.105.165149">10.1103/PhysRevB.105.165149</a>.
  short: S. De Nicola, A. Michailidis, M. Serbyn, Physical Review B 105 (2022).
date_created: 2022-04-28T08:06:10Z
date_published: 2022-04-15T00:00:00Z
date_updated: 2023-08-03T06:33:33Z
day: '15'
department:
- _id: MaSe
doi: 10.1103/PhysRevB.105.165149
ec_funded: 1
external_id:
  arxiv:
  - '2112.11273'
  isi:
  - '000806812400004'
intvolume: '       105'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: ' https://doi.org/10.48550/arXiv.2112.11273'
month: '04'
oa: 1
oa_version: Preprint
project:
- _id: 23841C26-32DE-11EA-91FC-C7463DDC885E
  call_identifier: H2020
  grant_number: '850899'
  name: 'Non-Ergodic Quantum Matter: Universality, Dynamics and Control'
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: Physical Review B
publication_identifier:
  eisbn:
  - 2469-9969
  issn:
  - 2469-9950
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
status: public
title: Entanglement and precession in two-dimensional dynamical quantum phase transitions
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 105
year: '2022'
...
---
_id: '9048'
abstract:
- lang: eng
  text: The analogy between an equilibrium partition function and the return probability
    in many-body unitary dynamics has led to the concept of dynamical quantum phase
    transition (DQPT). DQPTs are defined by nonanalyticities in the return amplitude
    and are present in many models. In some cases, DQPTs can be related to equilibrium
    concepts, such as order parameters, yet their universal description is an open
    question. In this Letter, we provide first steps toward a classification of DQPTs
    by using a matrix product state description of unitary dynamics in the thermodynamic
    limit. This allows us to distinguish the two limiting cases of “precession” and
    “entanglement” DQPTs, which are illustrated using an analytical description in
    the quantum Ising model. While precession DQPTs are characterized by a large entanglement
    gap and are semiclassical in their nature, entanglement DQPTs occur near avoided
    crossings in the entanglement spectrum and can be distinguished by a complex pattern
    of nonlocal correlations. We demonstrate the existence of precession and entanglement
    DQPTs beyond Ising models, discuss observables that can distinguish them, and
    relate their interplay to complex DQPT phenomenology.
acknowledgement: "S. D. N. acknowledges funding from the Institute of Science and
  Technology (IST) Austria and from the European Union’s Horizon 2020 Research and
  Innovation Programme under the Marie Skłodowska-Curie Grant Agreement No. 754411.
  A. M. and M. S. were supported by the European Research Council (ERC) under the
  European Union’s Horizon 2020 Research and\r\nInnovation Programme (Grant Agreement
  No. 850899)."
article_number: '040602'
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Stefano
  full_name: De Nicola, Stefano
  id: 42832B76-F248-11E8-B48F-1D18A9856A87
  last_name: De Nicola
  orcid: 0000-0002-4842-6671
- first_name: Alexios
  full_name: Michailidis, Alexios
  id: 36EBAD38-F248-11E8-B48F-1D18A9856A87
  last_name: Michailidis
  orcid: 0000-0002-8443-1064
- first_name: Maksym
  full_name: Serbyn, Maksym
  id: 47809E7E-F248-11E8-B48F-1D18A9856A87
  last_name: Serbyn
  orcid: 0000-0002-2399-5827
citation:
  ama: De Nicola S, Michailidis A, Serbyn M. Entanglement view of dynamical quantum
    phase transitions. <i>Physical Review Letters</i>. 2021;126(4). doi:<a href="https://doi.org/10.1103/physrevlett.126.040602">10.1103/physrevlett.126.040602</a>
  apa: De Nicola, S., Michailidis, A., &#38; Serbyn, M. (2021). Entanglement view
    of dynamical quantum phase transitions. <i>Physical Review Letters</i>. American
    Physical Society. <a href="https://doi.org/10.1103/physrevlett.126.040602">https://doi.org/10.1103/physrevlett.126.040602</a>
  chicago: De Nicola, Stefano, Alexios Michailidis, and Maksym Serbyn. “Entanglement
    View of Dynamical Quantum Phase Transitions.” <i>Physical Review Letters</i>.
    American Physical Society, 2021. <a href="https://doi.org/10.1103/physrevlett.126.040602">https://doi.org/10.1103/physrevlett.126.040602</a>.
  ieee: S. De Nicola, A. Michailidis, and M. Serbyn, “Entanglement view of dynamical
    quantum phase transitions,” <i>Physical Review Letters</i>, vol. 126, no. 4. American
    Physical Society, 2021.
  ista: De Nicola S, Michailidis A, Serbyn M. 2021. Entanglement view of dynamical
    quantum phase transitions. Physical Review Letters. 126(4), 040602.
  mla: De Nicola, Stefano, et al. “Entanglement View of Dynamical Quantum Phase Transitions.”
    <i>Physical Review Letters</i>, vol. 126, no. 4, 040602, American Physical Society,
    2021, doi:<a href="https://doi.org/10.1103/physrevlett.126.040602">10.1103/physrevlett.126.040602</a>.
  short: S. De Nicola, A. Michailidis, M. Serbyn, Physical Review Letters 126 (2021).
date_created: 2021-02-01T09:20:00Z
date_published: 2021-01-29T00:00:00Z
date_updated: 2023-09-05T12:08:58Z
day: '29'
ddc:
- '530'
department:
- _id: MaSe
doi: 10.1103/physrevlett.126.040602
ec_funded: 1
external_id:
  arxiv:
  - '2008.04894'
  isi:
  - '000613148200001'
file:
- access_level: open_access
  checksum: d9acbc502390ed7a97e631d23ae19ecd
  content_type: application/pdf
  creator: dernst
  date_created: 2021-02-03T12:47:04Z
  date_updated: 2021-02-03T12:47:04Z
  file_id: '9074'
  file_name: 2021_PhysicalRevLett_DeNicola.pdf
  file_size: 398075
  relation: main_file
  success: 1
file_date_updated: 2021-02-03T12:47:04Z
has_accepted_license: '1'
intvolume: '       126'
isi: 1
issue: '4'
keyword:
- General Physics and Astronomy
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
- _id: 23841C26-32DE-11EA-91FC-C7463DDC885E
  call_identifier: H2020
  grant_number: '850899'
  name: 'Non-Ergodic Quantum Matter: Universality, Dynamics and Control'
publication: Physical Review Letters
publication_identifier:
  eissn:
  - 1079-7114
  issn:
  - 0031-9007
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
status: public
title: Entanglement view of dynamical quantum phase transitions
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 126
year: '2021'
...
---
_id: '9158'
abstract:
- lang: eng
  text: While several tools have been developed to study the ground state of many-body
    quantum spin systems, the limitations of existing techniques call for the exploration
    of new approaches. In this manuscript we develop an alternative analytical and
    numerical framework for many-body quantum spin ground states, based on the disentanglement
    formalism. In this approach, observables are exactly expressed as Gaussian-weighted
    functional integrals over scalar fields. We identify the leading contribution
    to these integrals, given by the saddle point of a suitable effective action.
    Analytically, we develop a field-theoretical expansion of the functional integrals,
    performed by means of appropriate Feynman rules. The expansion can be truncated
    to a desired order to obtain analytical approximations to observables. Numerically,
    we show that the disentanglement approach can be used to compute ground state
    expectation values from classical stochastic processes. While the associated fluctuations
    grow exponentially with imaginary time and the system size, this growth can be
    mitigated by means of an importance sampling scheme based on knowledge of the
    saddle point configuration. We illustrate the advantages and limitations of our
    methods by considering the quantum Ising model in 1, 2 and 3 spatial dimensions.
    Our analytical and numerical approaches are applicable to a broad class of systems,
    bridging concepts from quantum lattice models, continuum field theory, and classical
    stochastic processes.
acknowledgement: "S D N would like to thank M J Bhaseen, J Chalker, B Doyon, V Gritsev,
  A Lamacraft,\r\nA Michailidis and M Serbyn for helpful feedback and stimulating
  conversations. S D N\r\nacknowledges funding from the Institute of Science and Technology
  (IST) Austria, and\r\nfrom the European Union’s Horizon 2020 research and innovation
  program under the\r\nMarie Sk\blodowska-Curie Grant Agreement No. 754411. S D N
  also acknowledges funding\r\nfrom the EPSRC Center for Doctoral Training in Cross-Disciplinary
  Approaches to Non-\r\nEquilibrium Systems (CANES) under Grant EP/L015854/1. S D
  N is grateful to IST\r\nAustria for providing open access funding."
article_number: '013101'
article_processing_charge: No
article_type: original
author:
- first_name: Stefano
  full_name: De Nicola, Stefano
  id: 42832B76-F248-11E8-B48F-1D18A9856A87
  last_name: De Nicola
  orcid: 0000-0002-4842-6671
citation:
  ama: 'De Nicola S. Disentanglement approach to quantum spin ground states: Field
    theory and stochastic simulation. <i>Journal of Statistical Mechanics: Theory
    and Experiment</i>. 2021;2021(1). doi:<a href="https://doi.org/10.1088/1742-5468/abc7c7">10.1088/1742-5468/abc7c7</a>'
  apa: 'De Nicola, S. (2021). Disentanglement approach to quantum spin ground states:
    Field theory and stochastic simulation. <i>Journal of Statistical Mechanics: Theory
    and Experiment</i>. IOP Publishing. <a href="https://doi.org/10.1088/1742-5468/abc7c7">https://doi.org/10.1088/1742-5468/abc7c7</a>'
  chicago: 'De Nicola, Stefano. “Disentanglement Approach to Quantum Spin Ground States:
    Field Theory and Stochastic Simulation.” <i>Journal of Statistical Mechanics:
    Theory and Experiment</i>. IOP Publishing, 2021. <a href="https://doi.org/10.1088/1742-5468/abc7c7">https://doi.org/10.1088/1742-5468/abc7c7</a>.'
  ieee: 'S. De Nicola, “Disentanglement approach to quantum spin ground states: Field
    theory and stochastic simulation,” <i>Journal of Statistical Mechanics: Theory
    and Experiment</i>, vol. 2021, no. 1. IOP Publishing, 2021.'
  ista: 'De Nicola S. 2021. Disentanglement approach to quantum spin ground states:
    Field theory and stochastic simulation. Journal of Statistical Mechanics: Theory
    and Experiment. 2021(1), 013101.'
  mla: 'De Nicola, Stefano. “Disentanglement Approach to Quantum Spin Ground States:
    Field Theory and Stochastic Simulation.” <i>Journal of Statistical Mechanics:
    Theory and Experiment</i>, vol. 2021, no. 1, 013101, IOP Publishing, 2021, doi:<a
    href="https://doi.org/10.1088/1742-5468/abc7c7">10.1088/1742-5468/abc7c7</a>.'
  short: 'S. De Nicola, Journal of Statistical Mechanics: Theory and Experiment 2021
    (2021).'
date_created: 2021-02-17T17:48:46Z
date_published: 2021-01-05T00:00:00Z
date_updated: 2023-08-07T13:46:28Z
day: '05'
ddc:
- '530'
department:
- _id: MaSe
doi: 10.1088/1742-5468/abc7c7
ec_funded: 1
external_id:
  isi:
  - '000605080300001'
file:
- access_level: open_access
  checksum: 64e2aae4837790db26e1dd1986c69c07
  content_type: application/pdf
  creator: dernst
  date_created: 2021-02-19T14:04:40Z
  date_updated: 2021-02-19T14:04:40Z
  file_id: '9172'
  file_name: 2021_JourStatMech_deNicola.pdf
  file_size: 1693609
  relation: main_file
  success: 1
file_date_updated: 2021-02-19T14:04:40Z
has_accepted_license: '1'
intvolume: '      2021'
isi: 1
issue: '1'
keyword:
- Statistics
- Probability and Uncertainty
- Statistics and Probability
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
publication: 'Journal of Statistical Mechanics: Theory and Experiment'
publication_identifier:
  issn:
  - 1742-5468
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
status: public
title: 'Disentanglement approach to quantum spin ground states: Field theory and stochastic
  simulation'
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: 2021
year: '2021'
...
---
_id: '9981'
abstract:
- lang: eng
  text: "The numerical simulation of dynamical phenomena in interacting quantum systems
    is a notoriously hard problem. Although a number of promising numerical methods
    exist, they often have limited applicability due to the growth of entanglement
    or the presence of the so-called sign problem. In this work, we develop an importance
    sampling scheme for the simulation of quantum spin dynamics, building on a recent
    approach mapping quantum spin systems to classical stochastic processes. The importance
    sampling scheme is based on identifying the classical trajectory that yields the
    largest contribution to a given quantum observable. An exact transformation is
    then carried out to preferentially sample trajectories that are close to the dominant
    one. We demonstrate that this approach is capable of reducing the temporal growth
    of fluctuations in the stochastic quantities, thus extending the range of accessible
    times and system sizes compared to direct sampling. We discuss advantages and
    limitations of the proposed approach, outlining directions\r\nfor further developments."
article_number: '048'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Stefano
  full_name: De Nicola, Stefano
  id: 42832B76-F248-11E8-B48F-1D18A9856A87
  last_name: De Nicola
  orcid: 0000-0002-4842-6671
citation:
  ama: De Nicola S. Importance sampling scheme for the stochastic simulation of quantum
    spin dynamics. <i>SciPost Physics</i>. 2021;11(3). doi:<a href="https://doi.org/10.21468/scipostphys.11.3.048">10.21468/scipostphys.11.3.048</a>
  apa: De Nicola, S. (2021). Importance sampling scheme for the stochastic simulation
    of quantum spin dynamics. <i>SciPost Physics</i>. SciPost. <a href="https://doi.org/10.21468/scipostphys.11.3.048">https://doi.org/10.21468/scipostphys.11.3.048</a>
  chicago: De Nicola, Stefano. “Importance Sampling Scheme for the Stochastic Simulation
    of Quantum Spin Dynamics.” <i>SciPost Physics</i>. SciPost, 2021. <a href="https://doi.org/10.21468/scipostphys.11.3.048">https://doi.org/10.21468/scipostphys.11.3.048</a>.
  ieee: S. De Nicola, “Importance sampling scheme for the stochastic simulation of
    quantum spin dynamics,” <i>SciPost Physics</i>, vol. 11, no. 3. SciPost, 2021.
  ista: De Nicola S. 2021. Importance sampling scheme for the stochastic simulation
    of quantum spin dynamics. SciPost Physics. 11(3), 048.
  mla: De Nicola, Stefano. “Importance Sampling Scheme for the Stochastic Simulation
    of Quantum Spin Dynamics.” <i>SciPost Physics</i>, vol. 11, no. 3, 048, SciPost,
    2021, doi:<a href="https://doi.org/10.21468/scipostphys.11.3.048">10.21468/scipostphys.11.3.048</a>.
  short: S. De Nicola, SciPost Physics 11 (2021).
date_created: 2021-09-02T11:49:47Z
date_published: 2021-09-02T00:00:00Z
date_updated: 2023-08-11T10:59:29Z
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title: Importance sampling scheme for the stochastic simulation of quantum spin dynamics
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---
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abstract:
- lang: eng
  text: Following on from our recent work, we investigate a stochastic approach to
    non-equilibrium quantum spin systems. We show how the method can be applied to
    a variety of physical observables and for different initial conditions. We provide
    exact formulae of broad applicability for the time-dependence of expectation values
    and correlation functions following a quantum quench in terms of averages over
    classical stochastic processes. We further explore the behavior of the classical
    stochastic variables in the presence of dynamical quantum phase transitions, including
    results for their distributions and correlation functions. We provide details
    on the numerical solution of the associated stochastic differential equations,
    and examine the growth of fluctuations in the classical description. We discuss
    the strengths and limitations of the current implementation of the stochastic
    approach and the potential for further development.
article_number: '013106'
article_processing_charge: No
article_type: original
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author:
- first_name: Stefano
  full_name: De Nicola, Stefano
  id: 42832B76-F248-11E8-B48F-1D18A9856A87
  last_name: De Nicola
  orcid: 0000-0002-4842-6671
- first_name: B.
  full_name: Doyon, B.
  last_name: Doyon
- first_name: M. J.
  full_name: Bhaseen, M. J.
  last_name: Bhaseen
citation:
  ama: 'De Nicola S, Doyon B, Bhaseen MJ. Non-equilibrium quantum spin dynamics from
    classical stochastic processes. <i>Journal of Statistical Mechanics: Theory and
    Experiment</i>. 2020;2020(1). doi:<a href="https://doi.org/10.1088/1742-5468/ab6093">10.1088/1742-5468/ab6093</a>'
  apa: 'De Nicola, S., Doyon, B., &#38; Bhaseen, M. J. (2020). Non-equilibrium quantum
    spin dynamics from classical stochastic processes. <i>Journal of Statistical Mechanics:
    Theory and Experiment</i>. IOP Publishing. <a href="https://doi.org/10.1088/1742-5468/ab6093">https://doi.org/10.1088/1742-5468/ab6093</a>'
  chicago: 'De Nicola, Stefano, B. Doyon, and M. J. Bhaseen. “Non-Equilibrium Quantum
    Spin Dynamics from Classical Stochastic Processes.” <i>Journal of Statistical
    Mechanics: Theory and Experiment</i>. IOP Publishing, 2020. <a href="https://doi.org/10.1088/1742-5468/ab6093">https://doi.org/10.1088/1742-5468/ab6093</a>.'
  ieee: 'S. De Nicola, B. Doyon, and M. J. Bhaseen, “Non-equilibrium quantum spin
    dynamics from classical stochastic processes,” <i>Journal of Statistical Mechanics:
    Theory and Experiment</i>, vol. 2020, no. 1. IOP Publishing, 2020.'
  ista: 'De Nicola S, Doyon B, Bhaseen MJ. 2020. Non-equilibrium quantum spin dynamics
    from classical stochastic processes. Journal of Statistical Mechanics: Theory
    and Experiment. 2020(1), 013106.'
  mla: 'De Nicola, Stefano, et al. “Non-Equilibrium Quantum Spin Dynamics from Classical
    Stochastic Processes.” <i>Journal of Statistical Mechanics: Theory and Experiment</i>,
    vol. 2020, no. 1, 013106, IOP Publishing, 2020, doi:<a href="https://doi.org/10.1088/1742-5468/ab6093">10.1088/1742-5468/ab6093</a>.'
  short: 'S. De Nicola, B. Doyon, M.J. Bhaseen, Journal of Statistical Mechanics:
    Theory and Experiment 2020 (2020).'
date_created: 2020-04-05T22:00:50Z
date_published: 2020-01-22T00:00:00Z
date_updated: 2023-08-18T10:27:15Z
day: '22'
ddc:
- '530'
department:
- _id: MaSe
doi: 10.1088/1742-5468/ab6093
ec_funded: 1
external_id:
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  - '1909.13142'
  isi:
  - '000520187500001'
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  date_updated: 2020-07-14T12:48:01Z
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  file_name: 2020_JournStatisticalMech_DeNicola.pdf
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has_accepted_license: '1'
intvolume: '      2020'
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language:
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month: '01'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
publication: 'Journal of Statistical Mechanics: Theory and Experiment'
publication_identifier:
  eissn:
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publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
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title: Non-equilibrium quantum spin dynamics from classical stochastic processes
type: journal_article
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volume: 2020
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...