Speaker: Clayton Peacock, PhD candidate at New York University's Center for Quantum Phenomena
Title: "Quantum Avalanches and Integrals of Motion in Disordered Systems"
Abstract
Anderson localization is a phenomenon in which a single quantum particle's eigenstates are exponentially localized due to spatial disorder, preventing its thermalization. This raises the question of whether interacting quantum systems can be similarly localized by disorder – a phenomenon dubbed many-body localization (MBL) and characterized by emergent local integrals of motion (LIOMs). Among the mechanisms thought to potentially destabilize MBL in the thermodynamic limit are “quantum avalanches,” in which rare Griffiths regions of lower disorder serve as thermalizing baths that delocalize LIOMs. While such regions are guaranteed to exist in the thermodynamic limit, observing their effect requires either very large system sizes or biased sampling. In this talk, we present numerical evidence of avalanches in 1D disordered spin chains using the latter approach, showing these systems are unstable at disorder strengths much higher than commonly believed (Physical Review B 108 (2), L020201). We also demonstrate how the Krylov subspace expansion can be leveraged to probe the existence of LIOMs. By calculating LIOMs in Krylov space for the 3D Anderson model, we show their existence in the localized regime is linked to an even-odd alternation of Lanczos coefficients and that the full transition is well captured by a disorder-averaged model of these coefficients (arXiv:2510.26920).
In this talk, we present numerical evidence of avalanches in 1D disordered spin chains using the latter approach, showing these systems are unstable at disorder strengths much higher than commonly believed. We also demonstrate how the Krylov subspace expansion can be leveraged to probe the existence of LIOMs. By calculating LIOMs in Krylov space for the 3D Anderson model, we show their existence in the localized regime is linked to an even-odd alternation of Lanczos coefficients and that the full transition is well captured by a disorder-averaged model of these coefficients.
