Similarity between a many-body quantum avalanche model and the ultrametric random matrix model

Šuntajs, Jan (author), Hopjan, Miroslav (author), De Roeck, Wojciech (author), Vidmar, Lev (author)

In the field of ergodicity-breaking phases, it has been recognized that quantum avalanches can destabilize many-body localization at a wide range of disorder strengths. This has in particular been demonstrated by the numerical study of a toy model, sometimes simply called the “avalanche model” or the “quantum sun model” [Phys. Rev. Lett. 129, 060602 (2022)], which consists of an ergodic seed coupled to a perfectly localized material. In this paper, we connect this toy model to a well-studied model in random matrix theory, the ultrametric ensemble. We conjecture that the models share the following features. (1) The location of the critical point may be predicted sharply by analytics. (2) On the localized site, both models exhibit Fock space localization. (3) There is a manifold of critical points. On the critical manifold, the eigenvectors exhibit nontrivial multifractal behavior that can be tuned by moving on the manifold. (4) The spectral statistics at criticality is intermediate between Poisson statistics and random matrix statistics, also tunable on the critical manifold. We confirm numerically these properties.

• Language: English
• Keywords: quantum statistical mechanics
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication version: Version of Record
• Publication date: 05.04.2024
• Year: 2024
• Number of pages: Str. 023030-1-023030-23
• Numbering: Vol. 6, iss. 2
• PID: 20.500.12556/RUL-155981
• UDC: 536.93
• ISSN on article: 2643-1564
• DOI: 10.1103/PhysRevResearch.6.023030
• COBISS.SI-ID: 193931523
• Publication date in RUL: 25.04.2024

Record is a part of a journal

• Title: Physical review research
• Publisher: American Phyisical Society
• ISSN: 2643-1564
• COBISS.SI-ID: 32822823

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.

Secondary language

• Language: Slovenian
• Keywords: kvantna statistična mehanika