Entanglement Properties and Quantum Phases for a Fermionic Disordered One-Dimensional Wire with Attractive...

Area of Science:

• Condensed Matter Physics
• Quantum Information Theory

Background:

• Disordered one-dimensional fermionic wires with attractive interactions exhibit localized and superconducting phases.
• Metallic behavior can emerge in the localized regime for systems smaller than the localization length.

Purpose of the Study:

• To differentiate between the superconducting and metallic phases in a disordered fermionic wire using entanglement entropy.
• To characterize the statistical properties of entanglement entropy distributions in these distinct phases.

Main Methods:

• Analysis of entanglement entropy distributions.
• Comparison of entanglement entropy distributions between superconducting and metallic regimes.
• Investigation of the second Rényi entropy distribution.

Main Results:

• The superconducting phase displays a distinct, strongly asymmetric entanglement entropy distribution.
• This distribution follows a Lévy α-stable law, contrasting with the Gaussian distribution observed in the metallic regime.
• Similar Lévy stable distribution characteristics are found for the second Rényi entropy.

Conclusions:

• Entanglement entropy provides a sensitive probe to distinguish between superconducting and metallic phases in disordered fermionic systems.
• The Lévy α-stable nature of entanglement entropy in the superconducting phase offers unique insights not detectable by other methods.