Spin Textures and Eigenstate Evolution of Isospectrally Patterned Lattices
Abstract
Isospectrally patterned lattices exhibit a composite band structure with a tunable ratio of localized versus delocalized eigenstates that is controlled by the underlying phase gradient. We show that the lattice Hamiltonian can be interpreted as that of a single spin which, exposed to a rotating magnetic field, hops across the lattice with a spin flip. In the low- and high-energy part of the band, the localized states show an envelope of oscillatory character separated by quasi-nodes. Spin peaks occur at the locations of these quasi-nodes and provide a unique spin texture to the eigenstates, which becomes increasingly complex with increasing degree of excitation. The crossover from localization to delocalization and vice versa leaves its fingerprints in the Fourier spectrum of the eigenstates: the original bimodal frequency distribution widens with increasing degree of excitation, moves across the spectral window, and finally culminates in an extremely narrow frequency peak. In the course of this evolution, the spin texture undergoes a rearrangement transition involving different characteristic (ir)regular patterns which we quantify by considering the total variation of the local spin fluctuations. Our results demonstrate the variety of the spectral properties of isospectrally patterned lattices, which holds great prospect, in particular when considering higher lattice or cell dimensions.
Related
- One-Particle Resonances and Eigenstate Thermalization in Periodic Free-Fermion Lattices
- Full Eigenstate Thermalization in Quantum Field Theory and Gravitational Scrambling
- A random sampling method to test the weak Eigenstate Thermalization Hypothesis
- Full Eigenstate Thermalization in Quantum Field Theory: Free Cumulants and Gravitational Scrambling
- Dominant Eigenstate Isolation through Symmetry-Orbit Decoupling
BibTeX
@misc{schmelcher2026spin,
title = {{Spin Textures and Eigenstate Evolution of Isospectrally Patterned Lattices}},
author = {Peter Schmelcher},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2607.07502},
eprint = {2607.07502},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.07502},
}
RIS
TY - UNPB
TI - Spin Textures and Eigenstate Evolution of Isospectrally Patterned Lattices
AU - Peter Schmelcher
PY - 2026
DA - 2026/11/06
PB - arXiv
DO - 10.48550/arxiv.2607.07502
UR - https://arxiv.org/abs/2607.07502
AB - Isospectrally patterned lattices exhibit a composite band structure with a tunable ratio of localized versus delocalized eigenstates that is controlled by the underlying phase gradient. We show that the lattice Hamiltonian can be interpreted as that of a single spin which, exposed to a rotating magnetic field, hops across the lattice with a spin flip. In the low- and high-energy part of the band, the localized states show an envelope of oscillatory character separated by quasi-nodes. Spin peaks occur at the locations of these quasi-nodes and provide a unique spin texture to the eigenstates, which becomes increasingly complex with increasing degree of excitation. The crossover from localization to delocalization and vice versa leaves its fingerprints in the Fourier spectrum of the eigenstates: the original bimodal frequency distribution widens with increasing degree of excitation, moves across the spectral window, and finally culminates in an extremely narrow frequency peak. In the course of this evolution, the spin texture undergoes a rearrangement transition involving different characteristic (ir)regular patterns which we quantify by considering the total variation of the local spin fluctuations. Our results demonstrate the variety of the spectral properties of isospectrally patterned lattices, which holds great prospect, in particular when considering higher lattice or cell dimensions.
ER -