# Logarithmic entanglement growth in two-dimensional disordered fermionic systems

## TL;DR

This paper studies how entanglement entropy grows over time in two-dimensional disordered fermionic systems, revealing a regime of logarithmic growth before localization effects dominate, with different behaviors depending on the type of disorder.

## Contribution

It demonstrates the existence of an intermediate weak localization regime with logarithmic entanglement growth and analyzes the effects of potential and bond disorder near critical points.

## Key findings

- Logarithmic entanglement growth observed before Anderson localization.
- Additive logarithmic corrections to area and volume laws near percolation transition.
- Scaling behavior consistent with an infinite randomness fixed point.

## Abstract

We investigate the growth of the entanglement entropy $S_{\textrm{ent}}$ following global quenches in two-dimensional free fermion models with potential and bond disorder. For the potential disorder case we show that an intermediate weak localization regime exists in which $S_{\textrm{ent}}(t)$ grows logarithmically in time $t$ before Anderson localization sets in. For the case of binary bond disorder near the percolation transition we find additive logarithmic corrections to area and volume laws as well as a scaling at long times which is consistent with an infinite randomness fixed point.