Mobility edge in long-range interacting many-body localized systems

TL;DR

This paper investigates the mobility edge phenomenon in long-range interacting many-body localized systems, showing how disorder and interaction range influence localization and phase boundaries across the energy spectrum.

Contribution

It provides a comprehensive phase diagram analysis for long-range systems, highlighting the impact of interaction range on localization and introducing methods to mitigate finite-size effects.

Findings

Long-range interactions shift the mobility edge towards smaller disorder values.

The phase boundary depends on the type of transition, either second-order or Kosterlitz-Thouless.

Discarding some system information can reduce finite-size effects and align results with thermodynamic predictions.

Abstract

As disorder strength increases in quantum many-body systems a new phase of matter, the so-called anybody localization, emerges across the whole spectrum. This transition is energy dependent, a phenomenon known as mobility edge, such that the mid-spectrum eigenstates tend to localize at larger values of disorder in comparison to eigenstates near the edges of the spectrum. Many-body localization becomes more sophisticated in long-range interacting systems. Here, by focusing on several quantities, we draw the phase diagram as a function of disorder strength and energy spectrum, for a various range of interactions. Regardless of the underlying transition type, either second-order or Kosterlitz-Thouless, our analysis consistently determines the mobility edge, i.e. the phase boundary across the spectrum. We show that long-range interaction enhances the localization effect and shifts the phase boundary towards smaller values of disorder. In addition, we establish a hierarchy among the studied quantities concerning their corresponding transition boundary and critical exponents. Interestingly, we show that deliberately discarding some information of the system can mitigate finite-size effects and provide results in line with the analytical predictions at the thermodynamic limit.