Latent symmetry induced degeneracies

TL;DR

This paper introduces a method to explain energy degeneracies in physical systems through latent symmetries of an effective Hamiltonian, revealing hidden symmetry structures that account for degeneracies beyond obvious symmetries.

Contribution

It develops a framework linking degeneracies to latent symmetries via subsystem partitioning and local symmetries in Hamiltonian powers, with applications to rotational symmetry breaking.

Findings

Degeneracies can be explained by latent symmetries of an isospectral Hamiltonian.

Latent symmetries relate to local symmetries in Hamiltonian powers.

Controlled symmetry breaking preserves underlying latent symmetries.

Abstract

Degeneracies in the energy spectra of physical systems are commonly considered to be either of accidental character or induced by symmetries of the Hamiltonian. We develop an approach to explain degeneracies by tracing them back to symmetries of an isospectral effective Hamiltonian derived by subsystem partitioning. We provide an intuitive interpretation of such latent symmetries by relating them to corresponding local symmetries in the powers of the underlying Hamiltonian matrix. As an application, we relate the degeneracies induced by the rotation symmetry of a real Hamiltonian to a non-abelian latent symmetry group. It is demonstrated that the rotational symmetries can be broken in a controlled manner while maintaining the underlying more fundamental latent symmetry. This opens up the perspective of investigating accidental degeneracies in terms of latent symmetries.