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Voinea, C., Fan, R., Regnault, N. et al. (1 more author) (2024) Regularizing 3D conformal field theories via anyons on the fuzzy sphere. [Preprint - arXiv]
Abstract
Recently introduced ''fuzzy sphere'' method has enabled accurate numerical regularizations of certain three-dimensional (3D) conformal field theories (CFTs). The regularization is provided by the non-commutative geometry of the lowest Landau level filled by electrons, such that the charge is trivially gapped due to the Pauli exclusion principle at filling factor , while the electron spins encode the desired CFT. Successful applications of the fuzzy sphere to paradigmatic CFTs, such as the 3D Ising model, raise an important question: how finely tuned does the underlying electron system need to be? Here, we show that the 3D Ising CFT can also be realized at fractional electron fillings. In such cases, the CFT spectrum is intertwined with the charge-neutral spectrum of the underlying fractional quantum Hall (FQH) state -- a feature that is trivially absent in the previously studied case. Remarkably, we show that the mixing between the CFT spectrum and the FQH spectrum is strongly suppressed within the numerically-accessible system sizes. Moreover, we demonstrate that the CFT critical point is unaffected by the exchange statistics of the particles and by the nature of topological order in the charge sector. Our results set the stage for the fuzzy-sphere exploration of conformal critical points between topologically-ordered states.
Metadata
Item Type: | Preprint |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This is an open access preprint under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Physics and Astronomy (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 21 May 2025 12:57 |
Last Modified: | 21 May 2025 12:57 |
Published Version: | https://arxiv.org/abs/2411.15299 |
Identification Number: | 10.48550/arxiv.2411.15299 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:226919 |
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