Quantum Avalanches and Krylov-space integrals of motion in disordered systems

Anderson localization is a phenomenon in which a single quantum particle's eigenstates are exponentially localized due to spatial disorder. This begs the question of whether a disordered interacting system can be similarly localized, a phenomenon dubbed many-body localization (MBL).

Thermalization in the thermodynamic is believed to be due to ''quantum avalanches'', in which rare Griffiths regions serve as thermalizing baths. These regions, which are sure to exist in the thermodynamic limit, are rare by nature and thus to observe their effect one either needs to access very large system sizes or resort to biased sampling.

In this talk we present evidence of avalanches in numerical studies using the latter, and show these systems are unstable at disorder much larger than commonly believed (Physical Review B 108 (2), L020201). We will also briefly review the Krylov subspace expansion method as a probe of quantum chaos and the existence of localized integrals of motion (LIOMs) in Krylov space.