Fractional Chern insulator states in an isolated flat band of zero Chern number
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_ | 1866918259923615744 |
|---|---|
| author | Lin, Zuzhang Lu, Hongyu Yang, Wenqi Zhai, Dawei Yao, Wang |
| author_facet | Lin, Zuzhang Lu, Hongyu Yang, Wenqi Zhai, Dawei Yao, Wang |
| contents | A flat band with Chern number $C=0$, and well isolated from the rest of Hilbert space by a gap much larger than interaction strength, is a context that has not been regarded as relevant for fractional quantum Hall physics. In this work, we demonstrate the emergence of the fractional Chern insulator (FCI) states in such a trivial flat band, using large-scale exact diagonalization (ED) and infinite density matrix renormalization group (iDMRG) simulations. The $C=0$ isolated flat band is hosted by an anisotropic fluxed dice lattice. Both the quantum metric and Berry curvature of the $C=0$ flat band have a sharp peak at the $Γ$ point, whereas in the rest of the Brillouin zone (BZ) they mimic the quantum geometry of the lowest Landau level. We consider nearest-neighbor repulsion that is weak enough to ensure the isolated-band limit is always satisfied. From the projected ED simulations at $ν_\mathrm{F}=2/3$ electron filling of the flat band (i.e. $1/3$ hole filling), we find the unexpected FCI with 3-fold ground-state degeneracy and $σ_\mathrm{H}=-1/3 (e^2/h)$. The momentum space carrier distribution shows that the quantum metric peak tends to push the interacting holes away from $Γ$ point towards the BZ regions with the nearly ``ideal'' quantum geometry, underlying the formation of FCI in the $C=0$ flat band. Besides, when tuning the single-particle anisotropy such that the quantum geometry of the $C=0$ flat band becomes less sharp around $Γ$, we find the ground state becomes a charge density wave with tripled unit cell at $ν_\mathrm{F}=2/3$. Our two-band iDMRG simulations further corroborate the FCI in the isolated $C=0$ flat band, demonstrating in such parameter regime the fractionally quantized charge pumping upon flux insertion as well as the momentum-resolved entanglement spectrum characteristic of the $1/3$ Laughlin state. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09009 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractional Chern insulator states in an isolated flat band of zero Chern number Lin, Zuzhang Lu, Hongyu Yang, Wenqi Zhai, Dawei Yao, Wang Mesoscale and Nanoscale Physics Materials Science Strongly Correlated Electrons A flat band with Chern number $C=0$, and well isolated from the rest of Hilbert space by a gap much larger than interaction strength, is a context that has not been regarded as relevant for fractional quantum Hall physics. In this work, we demonstrate the emergence of the fractional Chern insulator (FCI) states in such a trivial flat band, using large-scale exact diagonalization (ED) and infinite density matrix renormalization group (iDMRG) simulations. The $C=0$ isolated flat band is hosted by an anisotropic fluxed dice lattice. Both the quantum metric and Berry curvature of the $C=0$ flat band have a sharp peak at the $Γ$ point, whereas in the rest of the Brillouin zone (BZ) they mimic the quantum geometry of the lowest Landau level. We consider nearest-neighbor repulsion that is weak enough to ensure the isolated-band limit is always satisfied. From the projected ED simulations at $ν_\mathrm{F}=2/3$ electron filling of the flat band (i.e. $1/3$ hole filling), we find the unexpected FCI with 3-fold ground-state degeneracy and $σ_\mathrm{H}=-1/3 (e^2/h)$. The momentum space carrier distribution shows that the quantum metric peak tends to push the interacting holes away from $Γ$ point towards the BZ regions with the nearly ``ideal'' quantum geometry, underlying the formation of FCI in the $C=0$ flat band. Besides, when tuning the single-particle anisotropy such that the quantum geometry of the $C=0$ flat band becomes less sharp around $Γ$, we find the ground state becomes a charge density wave with tripled unit cell at $ν_\mathrm{F}=2/3$. Our two-band iDMRG simulations further corroborate the FCI in the isolated $C=0$ flat band, demonstrating in such parameter regime the fractionally quantized charge pumping upon flux insertion as well as the momentum-resolved entanglement spectrum characteristic of the $1/3$ Laughlin state. |
| title | Fractional Chern insulator states in an isolated flat band of zero Chern number |
| topic | Mesoscale and Nanoscale Physics Materials Science Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2505.09009 |