Momentum-space entanglement after a quench in one-dimensional disordered fermionic systems

TL;DR

This study numerically explores how momentum-space entanglement evolves after a quench in disordered one-dimensional fermionic models, revealing dynamics dependent on the initial Fermi level and indicating the presence of delocalized states.

Contribution

It demonstrates the relationship between initial Fermi level and entanglement growth, highlighting the spectral signatures of delocalized states in disordered fermionic systems.

Findings

Logarithmic growth of entanglement entropy near delocalized states

Rapid saturation of entanglement entropy away from delocalized states

Decay of entanglement gap indicating delocalization presence

Abstract

We numerically investigate the momentum-space entanglement entropy and entanglement spectrum of the random-dimer model and its generalizations, which circumvent Anderson localization, after a quench in the Hamiltonian parameters. The type of dynamics that occurs depends on whether or not the Fermi level of the initial state is near the energy of the delocalized states present in these models. If the Fermi level of the initial state is near the energy of the delocalized states, we observe an interesting slow logarithmic-like growth of the momentum-space entanglement entropy followed by an eventual saturation. Otherwise, the momentum-space entanglement entropy is found to rapidly saturate. We also find that the momentum-space entanglement spectrum reveals the presence of delocalized states in these models for long times after the quench and the many-body entanglement gap decays logarithmically in time when the Fermi level is near the energy of the delocalized states.