Latent Symmetry Induced Degeneracies.

Area of Science:

• Quantum mechanics
• Spectroscopy
• Mathematical physics

Background:

• Energy spectrum degeneracies are typically attributed to accidental properties or Hamiltonian symmetries.
• Understanding the origin of these degeneracies is crucial for characterizing physical systems.

Purpose of the Study:

• To develop a novel approach for explaining energy spectrum degeneracies.
• To connect degeneracies to symmetries of an isospectral effective Hamiltonian derived via subsystem partitioning.
• To provide an intuitive interpretation of these latent symmetries.

Main Methods:

• Derivation of an isospectral effective Hamiltonian through subsystem partitioning.
• Analysis of local symmetries in powers of the Hamiltonian matrix.
• Application to degeneracies induced by rotation symmetry in real Hamiltonians.

Main Results:

• Degeneracies can be explained by tracing them back to latent symmetries of an effective Hamiltonian.
• Latent symmetries correspond to local symmetries in powers of the Hamiltonian matrix.
• Rotational symmetries in real Hamiltonians are linked to a non-Abelian latent symmetry group.
• Controlled breaking of rotational symmetries while preserving fundamental latent symmetry is demonstrated.

Conclusions:

• The developed approach provides a new framework for understanding energy degeneracies.
• Latent symmetries offer a deeper perspective on the origins of accidental degeneracies.
• This work opens avenues for investigating accidental degeneracies through the lens of latent symmetries.