Composite fermion theory: a microscopic derivation without Landau level projection
The composite fermion (CF) theory gives both a phenomenological description for many fractional quantum Hall (FQH) states, as well as a microscopic construction for large scale numerical calculation of these topological phases. The fundamental postulate of mapping FQH states of electrons to integer...
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| Format: | Journal Article |
| Language: | English |
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2023
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| Online Access: | https://hdl.handle.net/10356/166308 |
| _version_ | 1826116419502211072 |
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| author | Yang, Bo |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Yang, Bo |
| author_sort | Yang, Bo |
| collection | NTU |
| description | The composite fermion (CF) theory gives both a phenomenological description for many fractional quantum Hall (FQH) states, as well as a microscopic construction for large scale numerical calculation of these topological phases. The fundamental postulate of mapping FQH states of electrons to integer quantum Hall (IQH) states of CFs, however, was not formally established. The Landau level (LL) projection needed for the microscopic calculations is in some sense uncontrolled and unpredictable. We rigorously derive the unitary relationship between electrons and the CFs, showing the latter naturally emerge from special interactions within a single LL, without resorting to any projection by hand. In this framework, all FQH states topologically equivalent to those described by the conventional CF theory (e.g., the Jain series) have exact model Hamiltonians that can be explicitly derived, and we can easily generalize to FQH states from interacting CFs. Our derivations reveal fundamental connections between the CF theory and the pseudopotential/Jack polynomial constructions, and argue that all Abelian CF states are physically equivalent to the IQH states, while a plethora of non-Abelian CF states can be systematically constructed and classified. We also discuss about implications to experiments and effective field theory descriptions based on the descriptions with CFs as elementary particles. |
| first_indexed | 2024-10-01T04:11:26Z |
| format | Journal Article |
| id | ntu-10356/166308 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T04:11:26Z |
| publishDate | 2023 |
| record_format | dspace |
| spelling | ntu-10356/1663082023-04-24T15:34:49Z Composite fermion theory: a microscopic derivation without Landau level projection Yang, Bo School of Physical and Mathematical Sciences Institute of High Performance Computing, A*STAR Science::Physics Fractional Quantum Hall Effect Landau Levels The composite fermion (CF) theory gives both a phenomenological description for many fractional quantum Hall (FQH) states, as well as a microscopic construction for large scale numerical calculation of these topological phases. The fundamental postulate of mapping FQH states of electrons to integer quantum Hall (IQH) states of CFs, however, was not formally established. The Landau level (LL) projection needed for the microscopic calculations is in some sense uncontrolled and unpredictable. We rigorously derive the unitary relationship between electrons and the CFs, showing the latter naturally emerge from special interactions within a single LL, without resorting to any projection by hand. In this framework, all FQH states topologically equivalent to those described by the conventional CF theory (e.g., the Jain series) have exact model Hamiltonians that can be explicitly derived, and we can easily generalize to FQH states from interacting CFs. Our derivations reveal fundamental connections between the CF theory and the pseudopotential/Jack polynomial constructions, and argue that all Abelian CF states are physically equivalent to the IQH states, while a plethora of non-Abelian CF states can be systematically constructed and classified. We also discuss about implications to experiments and effective field theory descriptions based on the descriptions with CFs as elementary particles. Nanyang Technological University National Research Foundation (NRF) Published version This work is supported by the NTU Grant for Nanyang Assistant Professorship and the National Research Foundation, Singapore under the NRF Fellowship Award(No.NRF-NRFF12-2020005)NRF-NRFF12-2020- 005), and a Nanyang Technological University start-up Grant (NTU-SUG). 2023-04-21T05:33:57Z 2023-04-21T05:33:57Z 2022 Journal Article Yang, B. (2022). Composite fermion theory: a microscopic derivation without Landau level projection. Physical Review B, 106, 245126-. https://dx.doi.org/10.1103/PhysRevB.106.245126 1098-0121 https://hdl.handle.net/10356/166308 10.1103/PhysRevB.106.245126 106 245126 en NRF-NRFF12-2020005 Physical Review B © 2022 American Physical Society. All rights reserved. This paper was published in Physical Review B and is made available with permission of American Physical Society. application/pdf |
| spellingShingle | Science::Physics Fractional Quantum Hall Effect Landau Levels Yang, Bo Composite fermion theory: a microscopic derivation without Landau level projection |
| title | Composite fermion theory: a microscopic derivation without Landau level projection |
| title_full | Composite fermion theory: a microscopic derivation without Landau level projection |
| title_fullStr | Composite fermion theory: a microscopic derivation without Landau level projection |
| title_full_unstemmed | Composite fermion theory: a microscopic derivation without Landau level projection |
| title_short | Composite fermion theory: a microscopic derivation without Landau level projection |
| title_sort | composite fermion theory a microscopic derivation without landau level projection |
| topic | Science::Physics Fractional Quantum Hall Effect Landau Levels |
| url | https://hdl.handle.net/10356/166308 |
| work_keys_str_mv | AT yangbo compositefermiontheoryamicroscopicderivationwithoutlandaulevelprojection |