---
APC_amount: 3599,50 EUR
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
PlanS_conform: '1'
_id: '20646'
abstract:
- lang: eng
text: Describing general quantum many-body dynamics is a challenging task due to
the exponential growth of the Hilbert space with system size. The time-dependent
variational principle (TDVP) provides a powerful tool to tackle this task by projecting
quantum evolution onto a classical dynamical system within a variational manifold.
In classical systems, periodic orbits play a crucial role in understanding the
structure of the phase space and the long-term behavior of the system. However,
finding periodic orbits is generally difficult, and their existence and properties
in generic TDVP dynamics over matrix product states have remained largely unexplored.
In this work, we develop an algorithm to systematically identify and characterize
periodic orbits in TDVP dynamics. Applying our method to the periodically kicked
Ising model, we uncover both stable and unstable periodic orbits. We characterize
the Kolmogorov-Arnold-Moser tori in the vicinity of stable periodic orbits and
track the change of the periodic orbits as we modify the Hamiltonian parameters.
We observe that periodic orbits exist at any value of the coupling constant of
the kicked Ising model between prethermal and fully thermalizing regimes, but
their relevance to quantum dynamics and imprint on quantum eigenstates diminishes
as the system leaves the prethermal regime. Our results demonstrate that periodic
orbits provide valuable insights into the TDVP approximation of quantum many-body
evolution and establish a closer connection between quantum and classical chaos.
acknowledgement: We acknowledge useful discussions with C. Kollath, A. Green, and
D. Huse. E.P., M.L., and M.S. acknowledge support by the European Research Council
under the European Union’s Horizon 2020 research and innovation program (Grant Agreement
No. 850899). This research was funded in whole or in part by the Austrian Science
Fund (FWF) (Grant No. 10.55776/COE1). For open access purposes, the author has applied
a CC BY public copyright license to any author accepted manuscript version arising
from this submission. M.L. acknowledges support by the Deutsche Forschungsgemeinschaft
(DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC-2111—390814868.
This research was supported in part by National Science Foundation (NSF) Grant No.
PHY-2309135 to the Kavli Institute for Theoretical Physics (KITP) and by the Erwin
Schrödinger International Institute for Mathematics and Physics (ESI).
article_number: '040333'
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Elena
full_name: Petrova, Elena
id: 0ac84990-897b-11ed-a09c-f5abb56a4ede
last_name: Petrova
- first_name: Marko
full_name: Ljubotina, Marko
id: F75EE9BE-5C90-11EA-905D-16643DDC885E
last_name: Ljubotina
orcid: 0000-0003-0038-7068
- first_name: Gökhan
full_name: Yalniz, Gökhan
id: 66E74FA2-D8BF-11E9-8249-8DE2E5697425
last_name: Yalniz
orcid: 0000-0002-8490-9312
- first_name: Maksym
full_name: Serbyn, Maksym
id: 47809E7E-F248-11E8-B48F-1D18A9856A87
last_name: Serbyn
orcid: 0000-0002-2399-5827
citation:
ama: Petrova E, Ljubotina M, Yalniz G, Serbyn M. Finding periodic orbits in projected
quantum many-body dynamics. PRX Quantum. 2025;6(4). doi:10.1103/tldp-kvkd
apa: Petrova, E., Ljubotina, M., Yalniz, G., & Serbyn, M. (2025). Finding periodic
orbits in projected quantum many-body dynamics. PRX Quantum. American Physical
Society. https://doi.org/10.1103/tldp-kvkd
chicago: Petrova, Elena, Marko Ljubotina, Gökhan Yalniz, and Maksym Serbyn. “Finding
Periodic Orbits in Projected Quantum Many-Body Dynamics.” PRX Quantum.
American Physical Society, 2025. https://doi.org/10.1103/tldp-kvkd.
ieee: E. Petrova, M. Ljubotina, G. Yalniz, and M. Serbyn, “Finding periodic orbits
in projected quantum many-body dynamics,” PRX Quantum, vol. 6, no. 4. American
Physical Society, 2025.
ista: Petrova E, Ljubotina M, Yalniz G, Serbyn M. 2025. Finding periodic orbits
in projected quantum many-body dynamics. PRX Quantum. 6(4), 040333.
mla: Petrova, Elena, et al. “Finding Periodic Orbits in Projected Quantum Many-Body
Dynamics.” PRX Quantum, vol. 6, no. 4, 040333, American Physical Society,
2025, doi:10.1103/tldp-kvkd.
short: E. Petrova, M. Ljubotina, G. Yalniz, M. Serbyn, PRX Quantum 6 (2025).
corr_author: '1'
date_created: 2025-11-14T09:40:52Z
date_published: 2025-11-12T00:00:00Z
date_updated: 2026-05-20T07:59:04Z
day: '12'
ddc:
- '539'
department:
- _id: GradSch
- _id: BjHo
- _id: MaSe
doi: 10.1103/tldp-kvkd
ec_funded: 1
external_id:
arxiv:
- '2504.12472'
isi:
- '001616473700003'
file:
- access_level: open_access
checksum: 5d6d04ac518b4118405334e1ddc7a56d
content_type: application/pdf
creator: gyalniz
date_created: 2025-11-14T09:44:10Z
date_updated: 2025-11-14T09:44:10Z
file_id: '20647'
file_name: tldp-kvkd.pdf
file_size: 2504713
relation: main_file
success: 1
file_date_updated: 2025-11-14T09:44:10Z
has_accepted_license: '1'
intvolume: ' 6'
isi: 1
issue: '4'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
project:
- _id: 23841C26-32DE-11EA-91FC-C7463DDC885E
call_identifier: H2020
grant_number: '850899'
name: 'Non-Ergodic Quantum Matter: Universality, Dynamics and Control'
- _id: 3AC91DDA-15DF-11EA-824D-93A3E7B544D1
call_identifier: FWF
name: FWF Open Access Fund
publication: PRX Quantum
publication_identifier:
eissn:
- 2691-3399
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
related_material:
link:
- description: News on ISTA website
relation: press_release
url: https://ista.ac.at/en/news/reaching-for-the-quantum-scars/
scopus_import: '1'
status: public
title: Finding periodic orbits in projected quantum many-body dynamics
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: '2025'
...
---
APC_amount: 3711,01 EUR
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
_id: '18488'
abstract:
- lang: eng
text: The advancement of quantum simulators motivates the development of a theoretical
framework to assist with efficient state preparation in quantum many-body systems.
Generally, preparing a target entangled state via unitary evolution with time-dependent
couplings is a challenging task and very little is known about the existence of
solutions and their properties. In this work we develop a constructive approach
for preparing matrix product states (MPS) via continuous unitary evolution. We
provide an explicit construction of the operator that exactly implements the evolution
of a given MPS along a specified direction in its tangent space. This operator
can be written as a sum of local terms of finite range, yet it is in general non-Hermitian.
Relying on the explicit construction of the non-Hermitian generator of the dynamics,
we demonstrate the existence of a Hermitian sequence of operators that implements
the desired MPS evolution with an error that decreases exponentially with the
operator range. The construction is benchmarked on an explicit periodic trajectory
in a translationally invariant MPS manifold. We demonstrate that the Floquet unitary
generating the dynamics over one period of the trajectory features an approximate
MPS-like eigenstate embedded among a sea of thermalizing eigenstates. These results
show that our construction is not only useful for state preparation and control
of many-body systems, but also provides a generic route towards Floquet scars—periodically
driven models with quasilocal generators of dynamics that have exact MPS eigenstates
in their spectrum.
acknowledgement: We thank L. Piroli, S. Garratt, and A. Molnár for insightful discussions.
This research was funded in part by the European Research Council (ERC) under the
European Union’s Horizon 2020 research and innovation programme (Grant Agreements
No. 850899 and No. 863476), the Austrian Science Fund (FWF) (Grant DOIs 10.55776/COE1,
10.55776/P36305, and 10.55776/F71), and the European Union (NextGenerationEU). This
work was performed in part at the Aspen Center for Physics, which is supported by
National Science Foundation Grant PHY-2210452. This research was supported in part
by NSF Grant PHY-2309135 to the Kavli Institute for Theoretical Physics (KITP).
article_number: '040311'
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Marko
full_name: Ljubotina, Marko
id: F75EE9BE-5C90-11EA-905D-16643DDC885E
last_name: Ljubotina
orcid: 0000-0003-0038-7068
- first_name: Elena
full_name: Petrova, Elena
id: 0ac84990-897b-11ed-a09c-f5abb56a4ede
last_name: Petrova
- first_name: Norbert
full_name: Schuch, Norbert
last_name: Schuch
- first_name: Maksym
full_name: Serbyn, Maksym
id: 47809E7E-F248-11E8-B48F-1D18A9856A87
last_name: Serbyn
orcid: 0000-0002-2399-5827
citation:
ama: Ljubotina M, Petrova E, Schuch N, Serbyn M. Tangent space generators of matrix
product states and exact floquet quantum scars. PRX Quantum. 2024;5(4).
doi:10.1103/prxquantum.5.040311
apa: Ljubotina, M., Petrova, E., Schuch, N., & Serbyn, M. (2024). Tangent space
generators of matrix product states and exact floquet quantum scars. PRX Quantum.
American Physical Society. https://doi.org/10.1103/prxquantum.5.040311
chicago: Ljubotina, Marko, Elena Petrova, Norbert Schuch, and Maksym Serbyn. “Tangent
Space Generators of Matrix Product States and Exact Floquet Quantum Scars.” PRX
Quantum. American Physical Society, 2024. https://doi.org/10.1103/prxquantum.5.040311.
ieee: M. Ljubotina, E. Petrova, N. Schuch, and M. Serbyn, “Tangent space generators
of matrix product states and exact floquet quantum scars,” PRX Quantum,
vol. 5, no. 4. American Physical Society, 2024.
ista: Ljubotina M, Petrova E, Schuch N, Serbyn M. 2024. Tangent space generators
of matrix product states and exact floquet quantum scars. PRX Quantum. 5(4), 040311.
mla: Ljubotina, Marko, et al. “Tangent Space Generators of Matrix Product States
and Exact Floquet Quantum Scars.” PRX Quantum, vol. 5, no. 4, 040311, American
Physical Society, 2024, doi:10.1103/prxquantum.5.040311.
short: M. Ljubotina, E. Petrova, N. Schuch, M. Serbyn, PRX Quantum 5 (2024).
corr_author: '1'
date_created: 2024-10-29T16:04:05Z
date_published: 2024-10-23T00:00:00Z
date_updated: 2025-09-08T14:26:29Z
day: '23'
ddc:
- '530'
department:
- _id: MaSe
doi: 10.1103/prxquantum.5.040311
ec_funded: 1
external_id:
arxiv:
- '2403.12325'
isi:
- '001346198800001'
file:
- access_level: open_access
checksum: 2e057ba021744d0a74602517935326b3
content_type: application/pdf
creator: dernst
date_created: 2024-10-30T08:59:09Z
date_updated: 2024-10-30T08:59:09Z
file_id: '18489'
file_name: 2024_PRXQuantum_Ljubotina.pdf
file_size: 1151431
relation: main_file
success: 1
file_date_updated: 2024-10-30T08:59:09Z
has_accepted_license: '1'
intvolume: ' 5'
isi: 1
issue: '4'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
project:
- _id: 23841C26-32DE-11EA-91FC-C7463DDC885E
call_identifier: H2020
grant_number: '850899'
name: 'Non-Ergodic Quantum Matter: Universality, Dynamics and Control'
publication: PRX Quantum
publication_identifier:
eissn:
- 2691-3399
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Tangent space generators of matrix product states and exact floquet quantum
scars
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 5
year: '2024'
...
---
_id: '15002'
abstract:
- lang: eng
text: "The lattice Schwinger model, the discrete version of QED in \r\n1\r\n+\r\n1\r\n
dimensions, is a well-studied test bench for lattice gauge theories. Here, we
study the fractal properties of this model. We reveal the self-similarity of the
ground state, which allows us to develop a recurrent procedure for finding the
ground-state wave functions and predicting ground-state energies. We present the
results of recurrently calculating ground-state wave functions using the fractal
Ansatz and automized software package for fractal image processing. In certain
parameter regimes, just a few terms are enough for our recurrent procedure to
predict ground-state energies close to the exact ones for several hundreds of
sites. Our findings pave the way to understanding the complexity of calculating
many-body wave functions in terms of their fractal properties as well as finding
new links between condensed matter and high-energy lattice models."
acknowledgement: "We thank A. Bargov, I. Khaymovich, and V. Tiunova for fruitful discussions
and for useful comments. M. C. B. thanks S. Kühn for discussions about the phase
structure of the model. A. K. F. thanks V. Gritsev and A. Garkun for insightful
comments. E. V. P., E. S. T., and A. K. F. are\r\nsupported by the RSF Grant No.
20-42-05002 (studying the fractal Ansatz) and the Roadmap on Quantum Computing (Contract
No. 868-1.3-15/15-2021, October 5, 2021; calculating on GS energies). A. K. F. thanks
the Priority 2030 program at the NIST “MISIS” under the project No. K1-2022-027.
M. C. B. was partly funded by the Deutsche Forschungsgemeinschaft (DFG, German Research
Foundation) under Germany’s Excellence Strategy—EXC-2111–390814868."
article_number: '050401'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Elena
full_name: Petrova, Elena
id: 0ac84990-897b-11ed-a09c-f5abb56a4ede
last_name: Petrova
- first_name: Egor S.
full_name: Tiunov, Egor S.
last_name: Tiunov
- first_name: Mari Carmen
full_name: Bañuls, Mari Carmen
last_name: Bañuls
- first_name: Aleksey K.
full_name: Fedorov, Aleksey K.
last_name: Fedorov
citation:
ama: Petrova E, Tiunov ES, Bañuls MC, Fedorov AK. Fractal states of the Schwinger
model. Physical Review Letters. 2024;132(5). doi:10.1103/PhysRevLett.132.050401
apa: Petrova, E., Tiunov, E. S., Bañuls, M. C., & Fedorov, A. K. (2024). Fractal
states of the Schwinger model. Physical Review Letters. American Physical
Society. https://doi.org/10.1103/PhysRevLett.132.050401
chicago: Petrova, Elena, Egor S. Tiunov, Mari Carmen Bañuls, and Aleksey K. Fedorov.
“Fractal States of the Schwinger Model.” Physical Review Letters. American
Physical Society, 2024. https://doi.org/10.1103/PhysRevLett.132.050401.
ieee: E. Petrova, E. S. Tiunov, M. C. Bañuls, and A. K. Fedorov, “Fractal states
of the Schwinger model,” Physical Review Letters, vol. 132, no. 5. American
Physical Society, 2024.
ista: Petrova E, Tiunov ES, Bañuls MC, Fedorov AK. 2024. Fractal states of the Schwinger
model. Physical Review Letters. 132(5), 050401.
mla: Petrova, Elena, et al. “Fractal States of the Schwinger Model.” Physical
Review Letters, vol. 132, no. 5, 050401, American Physical Society, 2024,
doi:10.1103/PhysRevLett.132.050401.
short: E. Petrova, E.S. Tiunov, M.C. Bañuls, A.K. Fedorov, Physical Review Letters
132 (2024).
date_created: 2024-02-18T23:01:00Z
date_published: 2024-01-30T00:00:00Z
date_updated: 2025-09-04T12:02:33Z
day: '30'
department:
- _id: MaSe
doi: 10.1103/PhysRevLett.132.050401
external_id:
arxiv:
- '2201.10220'
isi:
- '001179276700003'
pmid:
- '38364163'
intvolume: ' 132'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2201.10220
month: '01'
oa: 1
oa_version: Preprint
pmid: 1
publication: Physical Review Letters
publication_identifier:
eissn:
- 1079-7114
issn:
- 0031-9007
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Fractal states of the Schwinger model
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 132
year: '2024'
...
---
_id: '13138'
abstract:
- lang: eng
text: "We consider the spin-\r\n1\r\n2\r\n Heisenberg chain (XXX model) weakly perturbed
away from integrability by an isotropic next-to-nearest neighbor exchange interaction.
Recently, it was conjectured that this model possesses an infinite tower of quasiconserved
integrals of motion (charges) [D. Kurlov et al., Phys. Rev. B 105, 104302 (2022)].
In this work we first test this conjecture by investigating how the norm of the
adiabatic gauge potential (AGP) scales with the system size, which is known to
be a remarkably accurate measure of chaos. We find that for the perturbed XXX
chain the behavior of the AGP norm corresponds to neither an integrable nor a
chaotic regime, which supports the conjectured quasi-integrability of the model.
We then prove the conjecture and explicitly construct the infinite set of quasiconserved
charges. Our proof relies on the fact that the XXX chain perturbed by next-to-nearest
exchange interaction can be viewed as a truncation of an integrable long-range
deformation of the Heisenberg spin chain."
acknowledgement: "The numerical computations in this work were performed using QuSpin
[83, 84]. We acknowledge useful discussions with Igor Aleiner, Boris Altshuler,
Jacopo de Nardis, Anatoli Polkovnikov, and Gora Shlyapnikov. We thank Piotr Sierant
and Dario Rosa for drawing our attention to Refs. [31, 42, 46] and Ref. [47], respectively.
We are grateful to an anonymous referee for very useful comments and for drawing
our attention to Refs. [80, 81]. The work of VG is part of the DeltaITP consortium,
a program of the Netherlands Organization for Scientific\r\nResearch (NWO) funded
by the Dutch Ministry of Education, Culture and Science (OCW). VG is also partially
supported by RSF 19-71-10092. The work of AT was supported by the ERC Starting Grant
101042293 (HEPIQ). RS acknowledges support from Slovenian Research Agency (ARRS)
- research programme P1-0402. "
article_number: '184312'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Pavel
full_name: Orlov, Pavel
last_name: Orlov
- first_name: Anastasiia
full_name: Tiutiakina, Anastasiia
last_name: Tiutiakina
- first_name: Rustem
full_name: Sharipov, Rustem
last_name: Sharipov
- first_name: Elena
full_name: Petrova, Elena
id: 0ac84990-897b-11ed-a09c-f5abb56a4ede
last_name: Petrova
- first_name: Vladimir
full_name: Gritsev, Vladimir
last_name: Gritsev
- first_name: Denis V.
full_name: Kurlov, Denis V.
last_name: Kurlov
citation:
ama: Orlov P, Tiutiakina A, Sharipov R, Petrova E, Gritsev V, Kurlov DV. Adiabatic
eigenstate deformations and weak integrability breaking of Heisenberg chain. Physical
Review B. 2023;107(18). doi:10.1103/PhysRevB.107.184312
apa: Orlov, P., Tiutiakina, A., Sharipov, R., Petrova, E., Gritsev, V., & Kurlov,
D. V. (2023). Adiabatic eigenstate deformations and weak integrability breaking
of Heisenberg chain. Physical Review B. American Physical Society. https://doi.org/10.1103/PhysRevB.107.184312
chicago: Orlov, Pavel, Anastasiia Tiutiakina, Rustem Sharipov, Elena Petrova, Vladimir
Gritsev, and Denis V. Kurlov. “Adiabatic Eigenstate Deformations and Weak Integrability
Breaking of Heisenberg Chain.” Physical Review B. American Physical Society,
2023. https://doi.org/10.1103/PhysRevB.107.184312.
ieee: P. Orlov, A. Tiutiakina, R. Sharipov, E. Petrova, V. Gritsev, and D. V. Kurlov,
“Adiabatic eigenstate deformations and weak integrability breaking of Heisenberg
chain,” Physical Review B, vol. 107, no. 18. American Physical Society,
2023.
ista: Orlov P, Tiutiakina A, Sharipov R, Petrova E, Gritsev V, Kurlov DV. 2023.
Adiabatic eigenstate deformations and weak integrability breaking of Heisenberg
chain. Physical Review B. 107(18), 184312.
mla: Orlov, Pavel, et al. “Adiabatic Eigenstate Deformations and Weak Integrability
Breaking of Heisenberg Chain.” Physical Review B, vol. 107, no. 18, 184312,
American Physical Society, 2023, doi:10.1103/PhysRevB.107.184312.
short: P. Orlov, A. Tiutiakina, R. Sharipov, E. Petrova, V. Gritsev, D.V. Kurlov,
Physical Review B 107 (2023).
date_created: 2023-06-18T22:00:46Z
date_published: 2023-05-01T00:00:00Z
date_updated: 2023-08-02T06:16:02Z
day: '01'
department:
- _id: GradSch
doi: 10.1103/PhysRevB.107.184312
external_id:
arxiv:
- '2303.00729'
isi:
- '001003686900004'
intvolume: ' 107'
isi: 1
issue: '18'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2303.00729
month: '05'
oa: 1
oa_version: Preprint
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: Adiabatic eigenstate deformations and weak integrability breaking of Heisenberg
chain
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 107
year: '2023'
...