The index of a pair of pure states and the interacting integer quantum Hall effect
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915389980540928 |
|---|---|
| author | Bachmann, Sven Shapiro, Jacob Tauber, Clément |
| author_facet | Bachmann, Sven Shapiro, Jacob Tauber, Clément |
| contents | We introduce the index $\mathcal{N}(ω_1,ω_2)$ of a pair of pure states on a unital C*-algebra, which is a generalization of the notion of the index of a pair of projections on a Hilbert space. We then show that the Hall conductance associated with an invertible state $ω$ of a two-dimensional interacting electronic system which is symmetric under $U(1)$ charge transformation may be written as the index $\mathcal{N}(ω,ω_D)$, where $ω_D$ is obtained from $ω$ by inserting a unit of magnetic flux. This exhibits the integrality and continuity properties of the Hall conductance in the context of general topological features of $\mathcal{N}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10807 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The index of a pair of pure states and the interacting integer quantum Hall effect Bachmann, Sven Shapiro, Jacob Tauber, Clément Mathematical Physics Operator Algebras Quantum Physics We introduce the index $\mathcal{N}(ω_1,ω_2)$ of a pair of pure states on a unital C*-algebra, which is a generalization of the notion of the index of a pair of projections on a Hilbert space. We then show that the Hall conductance associated with an invertible state $ω$ of a two-dimensional interacting electronic system which is symmetric under $U(1)$ charge transformation may be written as the index $\mathcal{N}(ω,ω_D)$, where $ω_D$ is obtained from $ω$ by inserting a unit of magnetic flux. This exhibits the integrality and continuity properties of the Hall conductance in the context of general topological features of $\mathcal{N}$. |
| title | The index of a pair of pure states and the interacting integer quantum Hall effect |
| topic | Mathematical Physics Operator Algebras Quantum Physics |
| url | https://arxiv.org/abs/2507.10807 |