On the K-theory of magnetic algebras: Iwatsuka case
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914965917532160 |
|---|---|
| author | De Nittis, Giuseppe Gomez, Jaime Ojito, Danilo Polo |
| author_facet | De Nittis, Giuseppe Gomez, Jaime Ojito, Danilo Polo |
| contents | In the tight-binding approximation, an Iwatsuka magnetic field is modeled by a function on $\mathbb{Z}^2$ with constant, but distinct values in the two parts of the lattice separated by a straight line of slope $α\in [-\infty,\infty]$. In this paper, the $K$-theory of the magnetic $C^*$-algebras generated by an Iwatsuka magnetic field for any possible $α$ is computed. One interesting aspect concerns the analysis of the behavior of the system in the transition from rational to irrational $α$. It turns out that when $α$ is irrational, the magnetic hull associated with the flux operator forms a Cantor set. On the other hand, for rational $α$ this set coincides with the two-point compactification of $\mathbb{Z}$. This characterization, along with the use of the Pimsner-Voiculescu exact sequence, is the main ingredient for the computation of the $K$-theory. Once the $K$-theory is known, with the use of the index theory one can deduce the bulk-interface correspondence for tight-binding Hamiltonians subjected to an Iwatsuka magnetic field. Notably, it occurs that the topological quantization of the interface currents remains independent of the slope $α$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04531 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the K-theory of magnetic algebras: Iwatsuka case De Nittis, Giuseppe Gomez, Jaime Ojito, Danilo Polo Operator Algebras Mathematical Physics K-Theory and Homology Primary: 81R60, Secondary: 46L80, 81R60, 19K56 In the tight-binding approximation, an Iwatsuka magnetic field is modeled by a function on $\mathbb{Z}^2$ with constant, but distinct values in the two parts of the lattice separated by a straight line of slope $α\in [-\infty,\infty]$. In this paper, the $K$-theory of the magnetic $C^*$-algebras generated by an Iwatsuka magnetic field for any possible $α$ is computed. One interesting aspect concerns the analysis of the behavior of the system in the transition from rational to irrational $α$. It turns out that when $α$ is irrational, the magnetic hull associated with the flux operator forms a Cantor set. On the other hand, for rational $α$ this set coincides with the two-point compactification of $\mathbb{Z}$. This characterization, along with the use of the Pimsner-Voiculescu exact sequence, is the main ingredient for the computation of the $K$-theory. Once the $K$-theory is known, with the use of the index theory one can deduce the bulk-interface correspondence for tight-binding Hamiltonians subjected to an Iwatsuka magnetic field. Notably, it occurs that the topological quantization of the interface currents remains independent of the slope $α$. |
| title | On the K-theory of magnetic algebras: Iwatsuka case |
| topic | Operator Algebras Mathematical Physics K-Theory and Homology Primary: 81R60, Secondary: 46L80, 81R60, 19K56 |
| url | https://arxiv.org/abs/2410.04531 |