Many-body delocalization transition and relaxation in a quantum dot

TL;DR

This paper investigates the transition between localized and delocalized many-body states in a quantum dot, analyzing the conditions for localization, the nature of the transition, and the relaxation dynamics of various quantum states.

Contribution

It determines the localization threshold in Fock space and characterizes the sharpness of the transition at large conductance, along with analyzing relaxation processes of different quantum states.

Findings

Localization threshold in Fock space identified.

Transition becomes sharp at large conductance.

Relaxation dynamics vary with state type and energy.

Abstract

We revisit the problem of quantum localization of many-body states in a quantum dot and the associated problem of relaxation of an excited state in a finite correlated electron system. We determine the localization threshold for the eigenstates in Fock space. We argue that the localization-delocalization transition (which manifests itself, e.g., in the statistics of many-body energy levels) becomes sharp in the limit of a large dimensionless conductance (or, equivalently, in the limit of weak interaction). We also analyze the temporal relaxation of quantum states of various types (a "hot-electron state", a "typical" many-body state, and a single-electron excitation added to a "thermal state") with energies below, at, and above the transition.