The Fock-space landscape of many-body localisation

TL;DR

This review explores the Fock-space perspective of many-body localisation, analyzing eigenstate correlations, the MBL transition, and connecting theoretical insights to real-space observables.

Contribution

It provides a comprehensive overview of the Fock-space approach to MBL, highlighting differences from Anderson localisation and proposing a scaling theory for the transition.

Findings

Eigenstate correlations differ between ergodic and MBL phases.

A scaling theory for the MBL transition based on Fock-space quantities.

Connections established between Fock-space analysis and real-space observables.

Abstract

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.