The Fock-space landscape of many-body localisation

Journal article : Review

This article reviews recent progress in understanding the physics of many-body localisation (MBL) in disordered and interacting quantum many-body systems, from the perspective of ergodicity breaking on the associated Fock space. This approach to MBL is underpinned by mapping the dynamics of the many-body system onto that of a fictitious single particle on the high-dimensional, correlated and disordered Fock-space graph; yet, as we elaborate, the problem is fundamentally different from that of conventional Anderson localisation on high-dimensional or hierarchical graphs. We discuss in detail the nature of eigenstate correlations on the Fock space, both static and dynamic, and in the ergodic and many-body localised phases as well as in the vicinity of the MBL transition. The latter in turn sheds light on the nature of the transition, and motivates a scaling theory for it in terms of Fock-space based quantities. We also illustrate how these quantities can be concretely connected to real-space observables. An overview is given of several analytical and numerical techniques which have proven important in developing a comprehensive picture. Finally, we comment on some open questions in the field of MBL where the Fock-space approach is likely to prove insightful.

Authors: Roy, S; Logan, DE

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: IOP Publishing
• Journal: Journal of Physics: Condensed Matter
• Volume: 37
• Issue: 7
• Article number: 073003
• Publication date: 2024-12-06
• Acceptance date: 2024-11-19
• DOI: 10.1088/1361-648x/ad94c3
• EISSN: 1361-648X
• ISSN: 0953-8984
• Language: English
• Keywords: disordered quantum systems; quantum phase transitions; many-body localisation
• Subtype: Review