Characterizing disordered fermion systems using the momentum-space entanglement spectrum

TL;DR

This paper introduces the momentum-space entanglement spectrum as a novel tool to characterize disordered fermion systems, revealing localization and phase transitions more effectively than traditional real-space methods.

Contribution

It proposes using the momentum-space entanglement spectrum to identify delocalized states and phase transitions in disordered fermion models, a new approach compared to existing real-space analyses.

Findings

Momentum-space entanglement spectrum indicates localization in 1D systems.

It reveals the position of delocalized states in the energy spectrum.

The method detects phase transitions between localized and delocalized phases.

Abstract

The use of quantum entanglement to study condensed matter systems has been flourishing in critical systems and topological phases. Additionally, using real-space entanglement entropies and entanglement spectra one can characterize localized and delocalized phases of disordered fermion systems. Here we instead propose the momentum-space entanglement spectrum as a means of characterizing disordered models. We show that localization in 1D arises from the momentum space entanglement between left and right movers and illustrate our methods using explicit models with spatially correlated disorder that exhibit phases which avoid complete Anderson localization. The momentum space entanglement spectrum clearly reveals the location of delocalized states in the energy spectrum and can be used as a signature of the phase transition between a delocalized and localized phase.