2024/01/18 by Peter Schmelcher, Schmelcher, Peter · 2 citations
Chemistry · Materials Science · Physics and Astronomy · #Advanced Chemical Physics Studies #Advanced NMR Techniques and Applications #FOS: Physical sciences #Other Condensed Matter (cond-mat.other) #Quantum Physics (quant-ph) #Solid-state spectroscopy and crystallography
paper · pdf · doi:10.48550/arxiv.2401.09807
openalex publication_date 2024/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.