Thermalizing and localized many-body quantum systems present two distinct dynamical phases of matter. Recently the fate of a localized system coupled to a thermalizing system viewed as a quantum bath received significant theoretical and experimental attention. In this work, we study a mobile impurity, representing a small quantum bath, that interacts locally with an Anderson insulator with a finite density of localized particles. Using static Hartree approximation to obtain an effective disorder strength, we formulate an analytic criterion for the perturbative stability of the localization. Next, we use an approximate dynamical Hartree method and the quasi-exact time-evolved block decimation (TEBD) algorithm to study the dynamics of the system. We find that the dynamical Hartree approach which completely ignores entanglement between the impurity and localized particles predicts the delocalization of the system. In contrast, the full numerical simulation of the unitary dynamics with TEBD suggests the stability of localization on numerically accessible timescales. Finally, using an extension of the density matrix renormalization group algorithm to excited states (DMRG-X), we approximate the highly excited eigenstates of the system. We find that the impurity remains localized in the eigenstates and entanglement is enhanced in a finite region around the position of the impurity, confirming the dynamical predictions. Dynamics and the DMRG-X results provide compelling evidence for the stability of localization.
Physical Review B
We thank M. Ljubotina for insightful discussions. P. B., A. M. and M. S. acknowledge support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 850899). D. A. was supported by the Swiss National Science Foundation and by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 864597). The development of parallel TEBD code was supported by S. Elefante from the Scientific Computing (SciComp) that is part of Scientific Service Units (SSU) of IST Austria. Some of the computations were performed on the Baobab cluster of the University of Geneva.
Brighi P, Michailidis A, Kirova K, Abanin DA, Serbyn M. Localization of a mobile impurity interacting with an Anderson insulator. Physical Review B. 2022;105(22). doi:10.1103/physrevb.105.224208
Brighi, P., Michailidis, A., Kirova, K., Abanin, D. A., & Serbyn, M. (2022). Localization of a mobile impurity interacting with an Anderson insulator. Physical Review B. American Physical Society. https://doi.org/10.1103/physrevb.105.224208
Brighi, Pietro, Alexios Michailidis, Kristina Kirova, Dmitry A. Abanin, and Maksym Serbyn. “Localization of a Mobile Impurity Interacting with an Anderson Insulator.” Physical Review B. American Physical Society, 2022. https://doi.org/10.1103/physrevb.105.224208.
P. Brighi, A. Michailidis, K. Kirova, D. A. Abanin, and M. Serbyn, “Localization of a mobile impurity interacting with an Anderson insulator,” Physical Review B, vol. 105, no. 22. American Physical Society, 2022.
Brighi P, Michailidis A, Kirova K, Abanin DA, Serbyn M. 2022. Localization of a mobile impurity interacting with an Anderson insulator. Physical Review B. 105(22), 224208.
Brighi, Pietro, et al. “Localization of a Mobile Impurity Interacting with an Anderson Insulator.” Physical Review B, vol. 105, no. 22, 224208, American Physical Society, 2022, doi:10.1103/physrevb.105.224208.
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