Disorder-free localization in quantum walks

B. Danacl*, Yalçlnkaya, B. Çakmak, G. Karpat, S. P. Kelly, A. L. Subaşl

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


The phenomenon of localization usually happens due to the existence of disorder in a medium. Nevertheless, certain quantum systems allow dynamical localization solely due to the nature of internal interactions. We study a discrete time quantum walker which exhibits disorder-free localization. The quantum walker moves on a one-dimensional lattice and interacts with on-site spins by coherently rotating them around a given axis at each step. Since the spins do not have dynamics of their own, the system poses the local spin components along the rotation axis as an extensive number of conserved moments. When the interaction is weak, the spread of the walker shows subdiffusive behavior having downscaled ballistic tails in the evolving probability distribution at intermediate timescales. However, as the interaction gets stronger the walker gets completely localized in total absence of disorder in both lattice and initial state. Using a matrix-product-state ansatz, we investigate the relaxation and entanglement dynamics of the on-site spins due to their coupling with the quantum walker. Surprisingly, we find that, even in the delocalized regime, entanglement growth and relaxation occur slowly, unlike majority of the other models displaying a localization transition.

Original languageEnglish
Article number022416
JournalPhysical Review A
Issue number2
Publication statusPublished - Feb 2021

Bibliographical note

Publisher Copyright:
© 2021 American Physical Society.


B.D. thanks Juan José García Ripoll for useful discussions on matrix product states. İ.Y. thanks A. Gábris for helpful discussions and the support by MŠMT under Grant No. RVO 14000 and the Czech Science Foundation under Grant No. GA CR 19-15744Y. A.L.S. benefited from the 2015 Ghent summer school on tensor networks and acknowledges the hospitality of CNLS. G.K. is supported by the BAGEP Award of the Science Academy, the TUBA-GEBIP Award of the Turkish Academy of Sciences, and also by the Technological Research Council of Turkey (TUBITAK) under Grant No. 117F317. B.Ç. is supported by the BAGEP Award of the Science Academy, the Technological Research Council of Turkey (TUBITAK) under Grant No. 117F317, and also by the Research Fund of Bahçeşehir University (BAUBAP) under Project No. BAP.2019.02.03.

FundersFunder number
Ministerstvo Školství, Mládeže a TělovýchovyRVO 14000
Grantová Agentura České RepublikyGA CR 19-15744Y


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