Entanglement between Distant Regions in Disordered Quantum Wires

The entanglement negativity for spinless fermions in a strongly disordered 1D Anderson model is studied. For two close regions, the negativity is log-normally distributed, and is suppressed by repulsive interactions. With increasing distance between the regions, the typical negativity decays, but there remains a peak in the distribution, also at high values, representing highly entangled distant regions. For intermediate distances, in the noninteracting case, two distinct peaks are observed. As a function of interaction strength, the two peaks merge into each other. The abundance and nature of these entangled regions is studied. The relation to resonances between single-particle eigenstates is demonstrated. Thus, although the system is strongly disordered, it is nevertheless possible to encounter two far-away regions which are entangled.