Localization as an Entanglement Phase Transition in Boundary-Driven Anderson Models

Area of Science:

• Condensed Matter Physics
• Quantum Phase Transitions
• Non-equilibrium Systems

Background:

• Anderson localization is a key quantum phase transition at zero temperature.
• Disordered systems driven far from equilibrium present open research questions.
• Previous work showed extensive mutual information in the diffusive phase of a driven Anderson model.

Purpose of the Study:

• To study the Anderson localization transition in a driven, non-interacting, 3D Anderson model.
• To investigate the behavior of entanglement measures across the localization transition in a non-equilibrium steady state.
• To introduce and analyze a new entanglement witness, mutual coherence, for fermionic systems.

Main Methods:

• Analysis of the Anderson model in a current-carrying non-equilibrium steady state.
• Investigation of mutual information and entanglement scaling across the localization transition.
• Introduction and application of mutual coherence as an entanglement witness for fermionic Gaussian states.
• Combination of analytical arguments and numerical simulations for finite-size scaling analysis.

Main Results:

• Extensive entanglement scaling was observed to persist at the localization critical point.
• A crossover to short-range (area-law) scaling was found in the localized phase.
• Mutual coherence was introduced as a lower bound for mutual information in fermionic Gaussian states.
• Finite-size scaling of mutual coherence across the transition was determined.

Conclusions:

• The study advances the understanding of entanglement phase transitions in open, driven systems.
• Results have implications for driven many-body localized systems and experimental studies of driven-disordered systems.
• Mutual coherence serves as a valuable tool for characterizing entanglement in fermionic systems.