# Non-interacting central site model: localization and logarithmic entanglement growth

## TL;DR

This paper studies a localized chain coupled to a central site, revealing partial delocalization, finite resonant sites, and a regime of logarithmic transport, with implications for understanding localization and entanglement.

## Contribution

It introduces a model of a localized chain coupled to a single central site, analyzing its localization properties and identifying a logarithmic transport regime.

## Key findings

- Finite number of resonant sites in the thermodynamic limit
- Multifractal eigenstates with frozen fractal spectrum
- Logarithmic in time transport regime for weak coupling

## Abstract

We investigate the stationary and dynamical behavior of an Anderson localized chain coupled to a single central bound state. The coupling to the central site partially dilutes the Anderson localized peak towards the nearly resonant sites. In particular, the number of resonantly coupled sites remains finite in the thermodynamic limit. This is further supported by a multifractal analysis of eigenstates that shows the frozen spectrum of fractal dimension, which is characteristic for localized phases in models with power-law hopping. Although the well-known Fano-resonance problem is seemingly similar to our system, it fails to describe it because of the absence of level repulsion within the energy spectrum. For weak coupling strengths to the central site, we identify a regime with a logarithmic in time transport of particles and information.