Non-ergodic Delocalized Phase With Poisson Level Statistics

Tóm tắt

Motivated by the many-body localization (MBL) phase in generic interacting disordered quantum systems, we develop a model simulating the same eigenstate structure like in MBL, but in the random-matrix setting. Demonstrating the absence of energy level repulsion (Poisson statistics), this model carries non-ergodic eigenstates, delocalized over the extensive number of configurations in the Hilbert space. On the above example, we formulate general conditions to a single-particle and random-matrix models in order to carry such states, based on the transparent generalization of the Anderson localization of single-particle states and multiple resonances.

Featured image: Motivated by the many-body localization phase, we develop a random-matrix model simulating the same eigenstate structure. In order to have multifractal delocalized state without level repulsion we combine a power-law decaying hopping with the amplitude scaling up with the matrix size with respect to the diagonal disorder. This makes the multiple resonances possible without leading to level repulsion.

Tóm tắt phổ biến

Many-body localization is a phenomenon, providing a unique possibility for an isolated interacting quantum system to avoid thermalization and to keep the information about its initial state.
Being the localization in the real space, many-body localization not only suppresses the transport, but also avoids repulsion of energy levels and makes eigenstates of an interacting system to be non-ergodic, but extended in the space of configurations (Hilbert space).
Facing the difficulties of describing many-body quantum systems, many researchers focus on the universal statistical description of the above phenomenon in a random-matrix setting.

Motivated by the many-body localization phase, we develop a random-matrix model simulating the same eigenstate structure.
Demonstrating the absence of energy level repulsion (Poisson statistics), this model carries non-ergodic eigenstates, delocalized over the extensive number of configurations in the Hilbert space.
Using the above example and a transparent generalization of the Anderson localization to multiple resonances, we formulate general conditions to realize non-ergodic states with Poisson level statistics.

► Dữ liệu BibTeX

@article{Tang2022nonergodic, doi = {10.22331/q-2022-06-09-733}, url = {https://doi.org/10.22331/q-2022-06-09-733}, title = {Non-ergodic delocalized phase with {P}oisson level statistics}, author = {Tang, Weichen and Khaymovich, Ivan M.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {6}, pages = {733}, month = jun, year = {2022} }

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Trích dẫn

[1] M. Tarzia, “Fully localized and partially delocalized states in the tails of Erdös-Rényi graphs in the critical regime”, Đánh giá vật lý B 105 17, 174201 (2022).

[2] Adway Kumar Das and Anandamohan Ghosh, “Nonergodic extended states in the β ensemble”, Đánh giá vật lý E 105 5, 054121 (2022).

[3] Vedant Motamarri, Alexander S. Gorsky, and Ivan M. Khaymovich, “Localization and fractality in disordered Russian Doll model”, arXiv: 2112.05066.

Các trích dẫn trên là từ SAO / NASA ADS (cập nhật lần cuối thành công 2022 / 06-09 07:42:17). Danh sách có thể không đầy đủ vì không phải tất cả các nhà xuất bản đều cung cấp dữ liệu trích dẫn phù hợp và đầy đủ.

Không thể tìm nạp Crossref trích dẫn bởi dữ liệu trong lần thử cuối cùng 2022 / 06-09 07:42:15: Không thể tìm nạp dữ liệu được trích dẫn cho 10.22331 / q-2022 / 06-09-733 từ Crossref. Điều này là bình thường nếu DOI đã được đăng ký gần đây.

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Non-ergodic delocalized phase with Poisson level statistics

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