Fractional Chern insulators on cylinders: Tao-Thouless states and beyond
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915587084517376 |
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| author | Palm, Felix A. Van Bastelaere, Chloé Vanderstraeten, Laurens |
| author_facet | Palm, Felix A. Van Bastelaere, Chloé Vanderstraeten, Laurens |
| contents | Topological phases in two-dimensional quantum lattice models are often studied on cylinders for revealing different topological properties and making the problem numerically tractable. This makes a proper understanding of finite-circumference effects crucial for reliably extrapolating the results to the thermodynamic limit. Using matrix product states, we investigate these effects for the Laughlin-1/2 phase in the Hofstadter-Bose-Hubbard model, which can be viewed as the lattice discretization of the bosonic quantum Hall problem in the continuum. We propose a scaling of the model's parameters with the cylinder circumference that simultaneously approaches the continuum and thermodynamic limits. We find that different scaling schemes yield distinct topological signatures: we either retrieve a spontaneous formation of charge density wave ordering reminiscent of the Tao-Thouless states, known from the continuum problem on thin cylinders, or we find uniform states with a topological degeneracy that can be identified as minimally entangled states known from studies of chiral spin liquids on cylinders. Finally, we carry out a similar analysis of the non-Abelian Moore-Read phase in the same model. Our results clarify the role of symmetries in numerical studies of topologically ordered states on cylinders and highlight the role of lattice effects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26671 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractional Chern insulators on cylinders: Tao-Thouless states and beyond Palm, Felix A. Van Bastelaere, Chloé Vanderstraeten, Laurens Strongly Correlated Electrons Topological phases in two-dimensional quantum lattice models are often studied on cylinders for revealing different topological properties and making the problem numerically tractable. This makes a proper understanding of finite-circumference effects crucial for reliably extrapolating the results to the thermodynamic limit. Using matrix product states, we investigate these effects for the Laughlin-1/2 phase in the Hofstadter-Bose-Hubbard model, which can be viewed as the lattice discretization of the bosonic quantum Hall problem in the continuum. We propose a scaling of the model's parameters with the cylinder circumference that simultaneously approaches the continuum and thermodynamic limits. We find that different scaling schemes yield distinct topological signatures: we either retrieve a spontaneous formation of charge density wave ordering reminiscent of the Tao-Thouless states, known from the continuum problem on thin cylinders, or we find uniform states with a topological degeneracy that can be identified as minimally entangled states known from studies of chiral spin liquids on cylinders. Finally, we carry out a similar analysis of the non-Abelian Moore-Read phase in the same model. Our results clarify the role of symmetries in numerical studies of topologically ordered states on cylinders and highlight the role of lattice effects. |
| title | Fractional Chern insulators on cylinders: Tao-Thouless states and beyond |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2510.26671 |