Stability and instability towards delocalization in many-body localization systems

By Wojciech De Roeck, F. Huveneers. 2016

339 citations recorded by the source corpus.

We propose a theory that describes quantitatively the (in)stability of fully many-body localization (MBL) systems due to ergodic, i.e., delocalized, grains, that can be, for example, due to disorder fluctuations. The theory is based on the ETH hypothesis and elementary notions of perturbation theory. The main idea is that we assume as much chaoticity as is consistent with conservation laws. The theory describes correctly—even without relying on the theory of local integrals of motion (LIOM)—the MBL phase in one dimension at strong disorder. It yields an explicit and quantitative picture of the spatial boundary between localized and ergodic systems. We provide numerical evidence for this picture. When the theory is taken to its extreme logical consequences, it predicts that the MBL phase is destabilised in the long time limit whenever (1) interactions decay slower than exponentially in d=1 and (2) always in d>1. Finer numerics is required to assess these predictions.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/253ff5c021917850e5386c67986cfec0a3aadfd5

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Ergodicity breaking transition in finite disordered spin chains (2020, methodology): “[83] W.”
Probing Slow Relaxation and Many-Body Localization in Two-Dimensional Quasiperiodic Systems (2017, background): “[5] on MBL does not depend strongly on dimensionality, it was recently argued that rare, locally thermal regions [15] in systems with true random disorder can destabilize the MBL phase in two dimensions.”
Many-body localization: An introduction and selected topics (2017, neutral): “…been extended to study time dynamics after a quench in the MBL phase [188 In a different interesting perspective, it was also proposed to construct local approximations to the lioms to deﬁne a shifted Hamiltonian, whose ground-state properties are studied using quantum Monte Carlo techniques…”
Localization from Hilbert space shattering: From theory to physical realizations (2020, background): “[59] Wojciech De Roeck and Fran çois Huveneers, “Stability and instability towards delocalization in many-body localization systems,” Phys.”
Avalanches and many-body resonances in many-body localized systems (2021, background): “[34] Wojciech De Roeck and François Huveneers, “Stability and instability towards delocalization in many-body localization systems,” Phys.”