Hall-on-Toric: Descendant Laughlin state in the chiral $\mathbb{Z}_p$ toric code
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917430037577728 |
|---|---|
| author | Schäfer, Robin Chamon, Claudio Laumann, Chris R. |
| author_facet | Schäfer, Robin Chamon, Claudio Laumann, Chris R. |
| contents | We demonstrate that the chiral $\mathbb{Z}_p$ toric code -- the quintessential model of topological order -- hosts additional, emergent topological phases when perturbed: descendant fractional quantum Hall-like states, which we term \textit{Hall-on-Toric}. These hierarchical states feature fractionalized $\mathbb{Z}_p$ charges and increased topological ground-state degeneracy. The Hall-on-Toric phases appear in the vicinity of the transitions between deconfined $\mathbb{Z}_p$ phases with different background charge per unit cell, in a fixed non-trivial flux background. We confirm their existence through extensive infinite density matrix renormalization group (iDMRG) simulations, analyzing the topological entanglement entropy, entanglement spectra, and a generalized Hall conductance. Remarkably, the Hall-on-Toric states remain robust even in the absence of $U(1)$ symmetry. Our findings reinforce the foundational interpretation of star and plaquette defects as magnetic and electric excitations, and reveal that this perspective extends to a much deeper level. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02035 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hall-on-Toric: Descendant Laughlin state in the chiral $\mathbb{Z}_p$ toric code Schäfer, Robin Chamon, Claudio Laumann, Chris R. Strongly Correlated Electrons We demonstrate that the chiral $\mathbb{Z}_p$ toric code -- the quintessential model of topological order -- hosts additional, emergent topological phases when perturbed: descendant fractional quantum Hall-like states, which we term \textit{Hall-on-Toric}. These hierarchical states feature fractionalized $\mathbb{Z}_p$ charges and increased topological ground-state degeneracy. The Hall-on-Toric phases appear in the vicinity of the transitions between deconfined $\mathbb{Z}_p$ phases with different background charge per unit cell, in a fixed non-trivial flux background. We confirm their existence through extensive infinite density matrix renormalization group (iDMRG) simulations, analyzing the topological entanglement entropy, entanglement spectra, and a generalized Hall conductance. Remarkably, the Hall-on-Toric states remain robust even in the absence of $U(1)$ symmetry. Our findings reinforce the foundational interpretation of star and plaquette defects as magnetic and electric excitations, and reveal that this perspective extends to a much deeper level. |
| title | Hall-on-Toric: Descendant Laughlin state in the chiral $\mathbb{Z}_p$ toric code |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2507.02035 |