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.

中文翻译：

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潜在对称性引起的简并性

物理系统能谱的简并性通常被认为是偶然性的，或者是由哈密顿量的对称性引起的。我们开发了一种方法来解释简并性，方法是将它们追溯到由子系统划分得出的等光谱有效哈密顿量的对称性。通过将潜在的对称性与基础汉密尔顿矩阵的幂中的对应局部对称性相关联，我们提供了这种潜在对称性的直观解释。作为一种应用，我们将由真实哈密顿量的旋转对称性引起的简并性与非阿贝尔隐性对称群相关联。已经证明，旋转对称性可以以受控的方式被破坏，同时保持潜在的更基本的潜在对称性。