Degenerate subspace localization and local symmetries

• URL: http://arxiv.org/abs/2401.09807v1
• Date: Thu, 18 Jan 2024 08:56:35 GMT
• Title: Degenerate subspace localization and local symmetries
• Authors: Peter Schmelcher
• Abstract summary: Domain specific localization of eigenstates has been a persistent observation for systems with local symmetries. We provide here an analysis of locally symmetric tight-binding Hamiltonian which attempts at identifying the key features that lead to the localized eigenstates.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Domain specific localization of eigenstates has been a persistent observation for systems with local symmetries. The underlying mechanism for this localization behaviour has however remained elusive. We provide here an analysis of locally reflection symmetric tight-binding Hamiltonian which attempts at identifying the key features that lead to the localized eigenstates. A weak coupling expansion of closed-form expressions for the eigenvectors demonstrates that the degeneracy of on-site energies occuring at the center of the locally symmetric domains represents the nucleus for eigenstates spreading across the domain. Since the symmetry-related subdomains constituting a locally symmetric domain are isospectral we encounter pairwise degenerate eigenvalues that split linearly with an increasing coupling strength of the subdomains. The coupling to the (non-symmetric) environment in an extended setup then leads to the survival of a certain system specific fraction of linearly splitting eigenvalues. The latter go hand in hand with the eigenstate localization on the locally symmetric domain. We provide a brief outlook addressing possible generalizations of local symmetry transformations while maintaining isospectrality.

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