Composite Fermion Theory of Fractional Chern Insulator Stability
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917193496657920 |
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| author | Hu, Xiaodong Ran, Ying Xiao, Di |
| author_facet | Hu, Xiaodong Ran, Ying Xiao, Di |
| contents | We develop a mean-field theory of the stability of fractional Chern insulators based on the dipole picture of composite fermions (CFs). We construct CFs by binding vortices to Bloch electrons and derive a CF single-particle Hamiltonian that describes a Hofstadter problem in the enlarged CF Hilbert space, with the trace-condition term emerging naturally in the small-$q$ limit as part of the CF Hamiltonian. Going beyond the small-$q$ limit, we apply our theory to twisted MoTe$_2$ and calculate its CF band structures. The resulting CF phase diagram matches closely with that from exact diagonalization, and the projected many-body wavefunctions achieve exceptionally high overlaps with the latter. Our theory provides both a microscopic understanding and a computationally efficient tool for identifying fractional Chern insulators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03915 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Composite Fermion Theory of Fractional Chern Insulator Stability Hu, Xiaodong Ran, Ying Xiao, Di Strongly Correlated Electrons Mesoscale and Nanoscale Physics We develop a mean-field theory of the stability of fractional Chern insulators based on the dipole picture of composite fermions (CFs). We construct CFs by binding vortices to Bloch electrons and derive a CF single-particle Hamiltonian that describes a Hofstadter problem in the enlarged CF Hilbert space, with the trace-condition term emerging naturally in the small-$q$ limit as part of the CF Hamiltonian. Going beyond the small-$q$ limit, we apply our theory to twisted MoTe$_2$ and calculate its CF band structures. The resulting CF phase diagram matches closely with that from exact diagonalization, and the projected many-body wavefunctions achieve exceptionally high overlaps with the latter. Our theory provides both a microscopic understanding and a computationally efficient tool for identifying fractional Chern insulators. |
| title | Composite Fermion Theory of Fractional Chern Insulator Stability |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2508.03915 |