Degenerate subspace localization and local symmetries
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913199454945280 |
|---|---|
| author | Schmelcher, Peter |
| author_facet | Schmelcher, Peter |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09807 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Degenerate subspace localization and local symmetries Schmelcher, Peter Quantum Physics Other Condensed Matter 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. |
| title | Degenerate subspace localization and local symmetries |
| topic | Quantum Physics Other Condensed Matter |
| url | https://arxiv.org/abs/2401.09807 |