Quantum States and Spectra of Small Cylindrical and Toroidal Lattices

Abstract:We examine the spectrum and quantum states of small lattices with cylindrical and toroidal topology subject to a scalar gauge potential that introduces a position dependent phase in the inter-site coupling. Equivalency of gauges assumed in infinite lattices is generally lost due to the periodic boundary conditions, and conditions that restore it are identified. We trace the impact of various system parameters including gauge choice, boundary conditions and inter-site coupling strengths, and an additional axial field. We find gauge dependent appearance of avoided crossings and persistent degeneracies, and we show their impact on the associated eigenstates. Smaller lattices develop prominent gaps in spectral lines associated with edge states, which are suppressed in the thermodynamic limit. Toroidal lattices have counterparts of most of the features observed in cylindrical lattices, but notably they display a transition from localization to delocalization determined by the relation between the field parameter and the number of lattice sites.

Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)

arXiv:2609.36711 [quant-ph]

(or arXiv:2609.36711v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.36711 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

J. Phys. B: At. Mol. Opt. Phys. 57 205301 (2024)

https://doi.org/10.1088/1361-6455/ad7552 Focus to learn more DOI(s) linking to related resources

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.