Emergent commensurability from Hilbert space truncation in fractional quantum Hall fluids
We show that model states of fractional quantum Hall fluids at all experimentally detected plateaus can be uniquely determined by imposing translational invariance with a particular scheme of Hilbert space truncation. The truncation is based on classical local exclusion conditions, motivated by cons...
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| Format: | Journal Article |
| Language: | English |
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2020
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| Online Access: | https://hdl.handle.net/10356/142494 |
| _version_ | 1826127180805963776 |
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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 | We show that model states of fractional quantum Hall fluids at all experimentally detected plateaus can be uniquely determined by imposing translational invariance with a particular scheme of Hilbert space truncation. The truncation is based on classical local exclusion conditions, motivated by constraints on physical measurements. The scheme allows us to identify filling factors, topological shifts, and clustering of topological quantum fluids universally without resorting to microscopic Hamiltonians. This prompts us to propose the notion of emergent commensurability as a fundamental property for many known fractional quantum Hall (FQH) states, which allows us to predict families of new FQH states that can be realized in principle. We also discuss the implications of certain missing states proposed from other phenomenological approaches, and suggest that the physics of the FQH effect could fundamentally arise from the algebraic structure of the Hilbert space in a single Landau level. |
| first_indexed | 2024-10-01T07:04:34Z |
| format | Journal Article |
| id | ntu-10356/142494 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:04:34Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | ntu-10356/1424942023-02-28T19:47:50Z Emergent commensurability from Hilbert space truncation in fractional quantum Hall fluids Yang, Bo School of Physical and Mathematical Sciences Institute of High Performance Computing, A*STAR Science::Physics Fractional Quantum Hall Effect Mesoscopics We show that model states of fractional quantum Hall fluids at all experimentally detected plateaus can be uniquely determined by imposing translational invariance with a particular scheme of Hilbert space truncation. The truncation is based on classical local exclusion conditions, motivated by constraints on physical measurements. The scheme allows us to identify filling factors, topological shifts, and clustering of topological quantum fluids universally without resorting to microscopic Hamiltonians. This prompts us to propose the notion of emergent commensurability as a fundamental property for many known fractional quantum Hall (FQH) states, which allows us to predict families of new FQH states that can be realized in principle. We also discuss the implications of certain missing states proposed from other phenomenological approaches, and suggest that the physics of the FQH effect could fundamentally arise from the algebraic structure of the Hilbert space in a single Landau level. Published version 2020-06-23T02:23:31Z 2020-06-23T02:23:31Z 2019 Journal Article Yang, B. (2019). Emergent commensurability from Hilbert space truncation in fractional quantum Hall fluids. Physical Review B, 100(24), 241302(R)-. doi:10.1103/PhysRevB.100.241302 2469-9950 https://hdl.handle.net/10356/142494 10.1103/PhysRevB.100.241302 2-s2.0-85076741665 24 100 en Physical Review B © 2019 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 Mesoscopics Yang, Bo Emergent commensurability from Hilbert space truncation in fractional quantum Hall fluids |
| title | Emergent commensurability from Hilbert space truncation in fractional quantum Hall fluids |
| title_full | Emergent commensurability from Hilbert space truncation in fractional quantum Hall fluids |
| title_fullStr | Emergent commensurability from Hilbert space truncation in fractional quantum Hall fluids |
| title_full_unstemmed | Emergent commensurability from Hilbert space truncation in fractional quantum Hall fluids |
| title_short | Emergent commensurability from Hilbert space truncation in fractional quantum Hall fluids |
| title_sort | emergent commensurability from hilbert space truncation in fractional quantum hall fluids |
| topic | Science::Physics Fractional Quantum Hall Effect Mesoscopics |
| url | https://hdl.handle.net/10356/142494 |
| work_keys_str_mv | AT yangbo emergentcommensurabilityfromhilbertspacetruncationinfractionalquantumhallfluids |