Many-body localization on finite generation fractal lattices

TL;DR

This paper investigates many-body localization phenomena on various finite generation fractal lattices, revealing how the transition depends on fractal dimension and local structure through spectral and entanglement analysis.

Contribution

It introduces a study of many-body localization on diverse fractal lattices, highlighting the influence of fractal dimension and structure on localization transition.

Findings

Localization transition varies with Hausdorff dimension.

Spectral and entanglement properties indicate phase change.

Transition point depends on lattice structure.

Abstract

We study many-body localization in a hardcore boson model in the presence of random disorder on finite generation fractal lattices with different Hausdorff dimensions and different local lattice structures. In particular, we consider the Vicsek, T-shaped, Sierpinski gasket, and modified Koch-curve fractal lattices. In the single-particle case, these systems display Anderson localization for arbitrary disorder strength if they are large enough. In the many-body case, the systems available to exact diagonalization exhibit a transition between a delocalized and localized regime, visible in the spectral and entanglement properties of these systems. The position of this transition depends on the Hausdorff dimension of the given fractal, as well as on its local structure.