Non-Cayley-tree model for quasiparticle decay in a quantum dot

TL;DR

This paper introduces an alternative model for quasiparticle decay in quantum dots that accounts for strong correlations and differs from the Cayley tree approach, enabling the study of localization transitions in Fock space.

Contribution

It presents a new model capturing correlations in quasiparticle decay, allowing analysis of localization transitions beyond the Cayley tree approximation.

Findings

The model exhibits a localization transition in Fock space.

It differs significantly from the Cayley tree model in recursion relations.

Large system analysis reveals new insights into quasiparticle decay dynamics.

Abstract

The decay of a quasiparticle in a confined geometry, resulting from electron-electron interactions, has been mapped onto the single-electron problem of diffusion on a Cayley tree by Altshuler et al. [Phys.Rev.Lett. 78, 2803 (1997)]. We study an alternative model, that captures the strong correlations between the self-energies of different excitations with the same number of quasiparticles. The model has a recursion relation for the single-particle density of states that is markedly different from the Cayley tree. It remains tractable enough that sufficiently large systems can be studied to observe the localization transition in Fock space predicted by Altshuler et al.