Spread complexity for measurement-induced non-unitary dynamics and Zeno effect

2024
journal article
article
1
dc.abstract.enUsing spread complexity and spread entropy, we study non-unitary quantum dynamics. For non-hermitian Hamiltonians, we extend the bi-Lanczos construction for the Krylov basis to the Schrödinger picture. Moreover, we implement an algorithm adapted to complex symmetric Hamiltonians. This reduces the computational memory requirements by half compared to the bi-Lanczos construction. We apply this construction to the one-dimensional tight-binding Hamiltonian subject to repeated measurements at fixed small time intervals, resulting in effective non-unitary dynamics. We find that the spread complexity initially grows with time, followed by an extended decay period and saturation. The choice of initial state determines the saturation value of complexity and entropy. In analogy to measurement-induced phase transitions, we consider a quench between hermitian and non-hermitian Hamiltonian evolution induced by turning on regular measurements at different frequencies. We find that as a function of the measurement frequency, the time at which the spread complexity starts growing increases. This time asymptotes to infinity when the time gap between measurements is taken to zero, indicating the onset of the quantum Zeno effect, according to which measurements impede time evolution.
dc.affiliationWydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki Teoretycznej
dc.contributor.authorBhattacharya, Aranya - 479612
dc.contributor.authorDas, Rathindra Nath
dc.contributor.authorDey, Bidyut
dc.contributor.authorErdmenger, Johanna
dc.date.accessioned2024-05-13T09:10:23Z
dc.date.available2024-05-13T09:10:23Z
dc.date.issued2024
dc.date.openaccess0
dc.description.accesstimew momencie opublikowania
dc.description.number3
dc.description.versionostateczna wersja wydawcy
dc.description.volume2024
dc.identifier.articleid179
dc.identifier.doi10.1007/JHEP03(2024)179
dc.identifier.eissn1029-8479
dc.identifier.issn1126-6708
dc.identifier.project2021/42/E/ST2/00234
dc.identifier.project390858490
dc.identifier.project258499086—SFB 1170
dc.identifier.project57552340
dc.identifier.projectMAXPLA/PHY/2018577
dc.identifier.projectSERB/PHY/2020334
dc.identifier.urihttps://ruj.uj.edu.pl/handle/item/339327
dc.languageeng
dc.language.containereng
dc.rightsUdzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa
dc.rights.licenceCC-BY
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/legalcode.pl
dc.share.typeotwarte czasopismo
dc.subject.enquantum dissipative systems
dc.subject.enlattice integrable models
dc.subject.enphase transitions
dc.subject.enintegrable hierarchies
dc.subtypeArticle
dc.titleSpread complexity for measurement-induced non-unitary dynamics and Zeno effect
dc.title.journalJournal of High Energy Physics
dc.typeJournalArticle
dspace.entity.typePublicationen
dc.abstract.en
Using spread complexity and spread entropy, we study non-unitary quantum dynamics. For non-hermitian Hamiltonians, we extend the bi-Lanczos construction for the Krylov basis to the Schrödinger picture. Moreover, we implement an algorithm adapted to complex symmetric Hamiltonians. This reduces the computational memory requirements by half compared to the bi-Lanczos construction. We apply this construction to the one-dimensional tight-binding Hamiltonian subject to repeated measurements at fixed small time intervals, resulting in effective non-unitary dynamics. We find that the spread complexity initially grows with time, followed by an extended decay period and saturation. The choice of initial state determines the saturation value of complexity and entropy. In analogy to measurement-induced phase transitions, we consider a quench between hermitian and non-hermitian Hamiltonian evolution induced by turning on regular measurements at different frequencies. We find that as a function of the measurement frequency, the time at which the spread complexity starts growing increases. This time asymptotes to infinity when the time gap between measurements is taken to zero, indicating the onset of the quantum Zeno effect, according to which measurements impede time evolution.
dc.affiliation
Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki Teoretycznej
dc.contributor.author
Bhattacharya, Aranya - 479612
dc.contributor.author
Das, Rathindra Nath
dc.contributor.author
Dey, Bidyut
dc.contributor.author
Erdmenger, Johanna
dc.date.accessioned
2024-05-13T09:10:23Z
dc.date.available
2024-05-13T09:10:23Z
dc.date.issued
2024
dc.date.openaccess
0
dc.description.accesstime
w momencie opublikowania
dc.description.number
3
dc.description.version
ostateczna wersja wydawcy
dc.description.volume
2024
dc.identifier.articleid
179
dc.identifier.doi
10.1007/JHEP03(2024)179
dc.identifier.eissn
1029-8479
dc.identifier.issn
1126-6708
dc.identifier.project
2021/42/E/ST2/00234
dc.identifier.project
390858490
dc.identifier.project
258499086—SFB 1170
dc.identifier.project
57552340
dc.identifier.project
MAXPLA/PHY/2018577
dc.identifier.project
SERB/PHY/2020334
dc.identifier.uri
https://ruj.uj.edu.pl/handle/item/339327
dc.language
eng
dc.language.container
eng
dc.rights
Udzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa
dc.rights.licence
CC-BY
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/legalcode.pl
dc.share.type
otwarte czasopismo
dc.subject.en
quantum dissipative systems
dc.subject.en
lattice integrable models
dc.subject.en
phase transitions
dc.subject.en
integrable hierarchies
dc.subtype
Article
dc.title
Spread complexity for measurement-induced non-unitary dynamics and Zeno effect
dc.title.journal
Journal of High Energy Physics
dc.type
JournalArticle
dspace.entity.typeen
Publication

* The migration of download and view statistics prior to the date of April 8, 2024 is in progress.

Views
8
Views per month
Views per city
Krakow
2
Downloads
bhattacharya_et-al_spread_complexity_for_measurement-induced_2024.pdf
1