Röntgen M, Pyzh M, Morfonios C V, Palaiodimopoulos N E, Diakonos F K, Schmelcher P
Zentrum für optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany.
Department of Physics, University of Athens, 15771 Athens, Greece.
Phys Rev Lett. 2021 May 7;126(18):180601. doi: 10.1103/PhysRevLett.126.180601.
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.
物理系统能谱中的简并通常被认为要么具有偶然性质，要么是由哈密顿量的对称性所导致。我们开发了一种方法，通过将简并追溯到通过子系统划分得到的等谱有效哈密顿量的对称性来解释简并。我们通过将这些潜在对称性与基础哈密顿矩阵幂次中的相应局部对称性联系起来，对其进行了直观解释。作为一个应用，我们将实哈密顿量的旋转对称性所导致的简并与一个非阿贝尔潜在对称群联系起来。结果表明，在保持更基本的潜在对称性的同时，可以以可控的方式打破旋转对称性。这为从潜在对称性的角度研究偶然简并开辟了前景。
