Entanglement scaling of excited states in large one-dimensional many-body localized systems

TL;DR

This paper investigates the entanglement properties of excited states in large one-dimensional many-body localized systems using a matrix product state algorithm, revealing a logarithmic entanglement scaling and evidence for a mobility edge.

Contribution

It introduces a matrix product state method for excited states in large MBL systems and provides extensive data on entanglement scaling and mobility edges.

Findings

Entanglement scales logarithmically with system size in the MBL phase.

The results support the existence of a mobility edge in the system.

Eigenstate thermalization hypothesis is examined and discussed.

Abstract

We study the properties of excited states in one-dimensional many-body localized (MBL) systems using a matrix product state algorithm. First, the method is tested for a large disordered non-interacting system, where for comparison we compute a quasi-exact reference solution via a Monte Carlo sampling of the single-particle levels. Thereafter, we present extensive data obtained for large interacting systems of L~100 sites and large bond dimensions chi~1700, which allows us to quantitatively analyze the scaling behavior of the entanglement S in the system. The MBL phase is characterized by a logarithmic growth (L)~log(L) over a large scale separating the regimes where volume and area laws hold. We check the validity of the eigenstate thermalization hypothesis. Our results are consistent with the existence of a mobility edge.