Spin-statistics relation and the Abelian braiding phase for anyons in fractional quantum Hall effect
Quasihole excitations in fractional quantum Hall (FQH) systems exhibit fractional statistics and fractional spin, but how the spin-statistics relation emerges from many-body physics remains poorly understood. Here we prove a spin-statistics relation using only FQH wave functions, on both the sphe...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/169897 |
| _version_ | 1826121444605558784 |
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| author | Trung, Ha Quang Wang, Yuzhu Yang, Bo |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Trung, Ha Quang Wang, Yuzhu Yang, Bo |
| author_sort | Trung, Ha Quang |
| collection | NTU |
| description | Quasihole excitations in fractional quantum Hall (FQH) systems exhibit
fractional statistics and fractional spin, but how the spin-statistics relation
emerges from many-body physics remains poorly understood. Here we prove a
spin-statistics relation using only FQH wave functions, on both the sphere and
disk geometry. In particular, the proof on the disk generalizes to all
quasiholes in realistic systems, which have a finite size and could be deformed
into arbitrary shapes. Different components of the quasihole spins are linked
to different conformal Hilbert spaces (CHS), which are nullspaces of model
Hamiltonians that host the respective FQH ground states and quasihole states.
Understanding how the intrinsic spin of the quasiholes is linked to different
CHS is crucial for the generalized spin-statistics relation that takes into
account the effect of metric deformation. In terms of the experimental
relevance, this enables us to study the effect of deformation and disorder that
introduces an additional source of Berry curvature, an aspect of anyon braiding
that has been largely neglected in previous literature. |
| first_indexed | 2024-10-01T05:32:45Z |
| format | Journal Article |
| id | ntu-10356/169897 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T05:32:45Z |
| publishDate | 2023 |
| record_format | dspace |
| spelling | ntu-10356/1698972023-08-14T15:34:42Z Spin-statistics relation and the Abelian braiding phase for anyons in fractional quantum Hall effect Trung, Ha Quang Wang, Yuzhu Yang, Bo School of Physical and Mathematical Sciences Science::Physics Finite Size Fractional Quantum Hall Effects Quasihole excitations in fractional quantum Hall (FQH) systems exhibit fractional statistics and fractional spin, but how the spin-statistics relation emerges from many-body physics remains poorly understood. Here we prove a spin-statistics relation using only FQH wave functions, on both the sphere and disk geometry. In particular, the proof on the disk generalizes to all quasiholes in realistic systems, which have a finite size and could be deformed into arbitrary shapes. Different components of the quasihole spins are linked to different conformal Hilbert spaces (CHS), which are nullspaces of model Hamiltonians that host the respective FQH ground states and quasihole states. Understanding how the intrinsic spin of the quasiholes is linked to different CHS is crucial for the generalized spin-statistics relation that takes into account the effect of metric deformation. In terms of the experimental relevance, this enables us to study the effect of deformation and disorder that introduces an additional source of Berry curvature, an aspect of anyon braiding that has been largely neglected in previous literature. 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 (NRF-NRFF12-2020-005), and a Nanyang Technological University start-up grant (NTU-SUG). 2023-08-14T02:13:31Z 2023-08-14T02:13:31Z 2023 Journal Article Trung, H. Q., Wang, Y. & Yang, B. (2023). Spin-statistics relation and the Abelian braiding phase for anyons in fractional quantum Hall effect. Physical Review B, 107(20), L201301-1-L201301-7. https://dx.doi.org/10.1103/PhysRevB.107.L201301 1098-0121 https://hdl.handle.net/10356/169897 10.1103/PhysRevB.107.L201301 2-s2.0-85161115770 20 107 L201301-1 L201301-7 en NRF-NRFF12-2020-005 NTU-SUG NAP Physical Review B © 2023 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 Finite Size Fractional Quantum Hall Effects Trung, Ha Quang Wang, Yuzhu Yang, Bo Spin-statistics relation and the Abelian braiding phase for anyons in fractional quantum Hall effect |
| title | Spin-statistics relation and the Abelian braiding phase for anyons in fractional quantum Hall effect |
| title_full | Spin-statistics relation and the Abelian braiding phase for anyons in fractional quantum Hall effect |
| title_fullStr | Spin-statistics relation and the Abelian braiding phase for anyons in fractional quantum Hall effect |
| title_full_unstemmed | Spin-statistics relation and the Abelian braiding phase for anyons in fractional quantum Hall effect |
| title_short | Spin-statistics relation and the Abelian braiding phase for anyons in fractional quantum Hall effect |
| title_sort | spin statistics relation and the abelian braiding phase for anyons in fractional quantum hall effect |
| topic | Science::Physics Finite Size Fractional Quantum Hall Effects |
| url | https://hdl.handle.net/10356/169897 |
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