Entanglement entropy distribution in the strongly disordered one-dimensional Anderson model

TL;DR

This paper investigates the entanglement entropy distribution in the canonical Anderson model with on-site disorder and interactions, revealing distinct features influenced by disorder and contrasting with bond-disordered models.

Contribution

It demonstrates how on-site disorder affects entanglement entropy distribution in the Anderson model, using DMRG and RSRG methods to analyze the differences from bond-disordered systems.

Findings

Broad peak at low entanglement values shifts lower with increased disorder

A narrower peak appears at ln(2), with no higher integer peaks observed

On-site disorder breaks boundary symmetry, altering the distribution shape

Abstract

The entanglement entropy distribution of strongly disordered one dimensional spin chains, which are equivalent to spinless fermions at half-filling on a bond (hopping) disordered one-dimensional Anderson model, has been shown to exhibit very distinct features such as peaks at integer multiplications of $\ln(2)$, essentially counting the number of singlets traversing the boundary. Here we show that for a canonical Anderson model with box distribution on-site disorder and repulsive nearest-neighbor interactions the entanglement entropy distribution also exhibits interesting features, albeit different than the distribution seen for the bond disordered Anderson model. The canonical Anderson model shows a broad peak at low entanglement values and one narrower peak at $\ln(2)$. Density matrix renormalization group (DMRG) calculations reveal this structure and the influence of the disorder strength and the interaction strength on its shape. A modified real space renormalization group (RSRG) method was used to get a better understanding of this behavior. As might be expected the peak centered at low values of entanglement entropy has a tendency to shift to lower values as disorder is enhanced. A second peak appears around the entanglement entropy value of $\ln(2)$,this peak is broadened and no additional peaks at higher integer multiplications of $\ln(2)$ are seen. We attribute the differences in the distribution between the canonical model and the broad hopping disorder to the influence of the on-site disorder which breaks the symmetry across the boundary.