Ground-state degeneracies leave recognizable topological scars in the electronic density

Area of Science:

• Quantum mechanics
• Computational physics
• Materials science

Background:

• Kohn-Sham density functional theory (KS DFT) models physical systems using a fictitious non-interacting particle system with an identical ground-state (GS) density.
• A key challenge in DFT is determining if exact KS calculations can detect and characterize GS degeneracies within the physical system.

Purpose of the Study:

• To investigate the capability of exact KS calculations to identify and characterize ground-state degeneracies.
• To explore the role of the ground-state density in revealing topological features related to degeneracies.

Main Methods:

• Theoretical analysis of the ground-state density.
• Examination of the ground-state density's behavior across a 2D parameter manifold of the external potential.

Main Results:

• Theoretical evidence indicates that the ground-state density is topologically scarred by degeneracies.
• These topological scars provide detailed information about the positions of degeneracies.
• The associated Berry phases can also be determined from these scars.

Conclusions:

• Exact KS calculations are capable of spotting and characterizing ground-state degeneracies.
• The ground-state density contains rich topological information crucial for understanding system degeneracies.