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Operator entanglement in local quantum circuits II: Solitons in chains of qubits
ID
Bertini, Bruno
(
Author
),
ID
Kos, Pavel
(
Author
),
ID
Prosen, Tomaž
(
Author
)
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https://scipost.org/10.21468/SciPostPhys.8.4.068
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Abstract
We provide exact results for the dynamics of local-operator entanglement in quantum circuits with two-dimensional wires featuring ultralocal solitons, i.e. single-site operators which, up to a phase, are simply shifted by the time evolution. We classify all circuits, allowing for ultralocal solitons and show that only dual-unitary circuits can feature moving ultralocal solitons. Then, we rigorously prove that if a circuit has an ultralocal soliton moving to the left (right), the entanglement of local operators initially supported on even (odd) sites saturates to a constant value and its dynamics can be computed exactly. Importantly, this does not bound the growth of complexity in chiral circuits, where solitons move only in one direction, say to the left. Indeed, in this case we observe numerically that operators on the odd sublattice have unbounded entanglement. Finally, we present a closed-form expression for the local-operator entanglement entropies in circuits with ultralocal solitons moving in both directions. Our results hold irrespectively of integrability.
Language:
English
Keywords:
entanglement
,
qubits
,
quantum many-body systems
Typology:
1.01 - Original Scientific Article
Organization:
FMF - Faculty of Mathematics and Physics
Publication status:
Published
Publication version:
Version of Record
Year:
2020
Number of pages:
23 str.
Numbering:
Vol. 8, art. no. 068
PID:
20.500.12556/RUL-116060
UDC:
530.145
ISSN on article:
2542-4653
DOI:
10.21468/SciPostPhys.8.4.068
COBISS.SI-ID:
14722819
Publication date in RUL:
12.05.2020
Views:
1036
Downloads:
363
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Record is a part of a journal
Title:
SciPost physics
Publisher:
SciPost Foundation
ISSN:
2542-4653
COBISS.SI-ID:
526154521
Licences
License:
CC BY 4.0, Creative Commons Attribution 4.0 International
Link:
http://creativecommons.org/licenses/by/4.0/
Description:
This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.
Licensing start date:
12.05.2020
Secondary language
Language:
Slovenian
Keywords:
kvantna prepletenost
,
kubiti
,
večdelčni sistemi
Projects
Funder:
EC - European Commission
Funding programme:
H2020
Project number:
694544
Name:
Open Many-body Non-Equilibrium Systems
Acronym:
OMNES
Funder:
ARRS - Slovenian Research Agency
Project number:
P1-0402
Name:
Matematična fizika
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