Bootstrapping the Quantum Hall problem Article Swipe
Qiang Gao
,
Ryan A. Lanzetta
,
Patrick J. Ledwith
,
Jie Wang
,
Eslam Khalaf
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2409.10619
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2409.10619
The bootstrap method aims to solve problems by imposing constraints on the space of physical observables, which often follow from physical assumptions such as positivity and symmetry. Here, we employ a bootstrap approach to study interacting electrons in the lowest Landau level by minimizing the energy as a function of the static structure factor subject to a set of constraints, bypassing the need to construct the full many-body wavefunction. This approach rigorously lower bounds the ground state energy, making it complementary to conventional variational upper bounds. We show that the lower bound we obtain is relatively tight, within at most 5\% from the ground state energy computed with exact diagonalization (ED) at small system sizes, and generally gets tighter as we include more constraints. In addition to energetics, our results reproduce the correct power law dependence of the pair correlation function at short distances and the existence of a large entanglement gap in the two-particle entanglement spectra for the Laughlin states at $ν= 1/3$. We further identify signatures of the composite Fermi liquid state close to half-filling. This shows that the bootstrap approach is capable, in principle, of describing non-trivial gapped topologically ordered, as well as gapless, phases. At the end, we will discuss possible extensions and limitations of this approach. Our work establishes numerical bootstrap as a promising method to study many-body phases in topological bands, paving the way to its application in moiré platforms where the energetic competition between fractional quantum anomalous Hall, symmetry broken, and gapless states remains poorly understood.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2409.10619
- https://arxiv.org/pdf/2409.10619
- OA Status
- green
- Cited By
- 1
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4403705015
All OpenAlex metadata
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https://openalex.org/W4403705015Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2409.10619Digital Object Identifier
- Title
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Bootstrapping the Quantum Hall problemWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2024Year of publication
- Publication date
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2024-09-16Full publication date if available
- Authors
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Qiang Gao, Ryan A. Lanzetta, Patrick J. Ledwith, Jie Wang, Eslam KhalafList of authors in order
- Landing page
-
https://arxiv.org/abs/2409.10619Publisher landing page
- PDF URL
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https://arxiv.org/pdf/2409.10619Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2409.10619Direct OA link when available
- Concepts
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Bootstrapping (finance), Quantum Hall effect, Quantum, Physics, Computer science, Theoretical physics, Mathematics, Quantum mechanics, Econometrics, Magnetic fieldTop concepts (fields/topics) attached by OpenAlex
- Cited by
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1Total citation count in OpenAlex
- Citations by year (recent)
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2025: 1Per-year citation counts (last 5 years)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.structure | 52 |
| abstract_inverted_index.symmetry. | 26 |
| abstract_inverted_index.dependence | 135 |
| abstract_inverted_index.describing | 188 |
| abstract_inverted_index.extensions | 205 |
| abstract_inverted_index.fractional | 241 |
| abstract_inverted_index.minimizing | 43 |
| abstract_inverted_index.positivity | 24 |
| abstract_inverted_index.principle, | 186 |
| abstract_inverted_index.relatively | 95 |
| abstract_inverted_index.rigorously | 71 |
| abstract_inverted_index.signatures | 167 |
| abstract_inverted_index.application | 232 |
| abstract_inverted_index.assumptions | 21 |
| abstract_inverted_index.competition | 239 |
| abstract_inverted_index.constraints | 9 |
| abstract_inverted_index.correlation | 139 |
| abstract_inverted_index.energetics, | 127 |
| abstract_inverted_index.establishes | 213 |
| abstract_inverted_index.interacting | 35 |
| abstract_inverted_index.limitations | 207 |
| abstract_inverted_index.non-trivial | 189 |
| abstract_inverted_index.topological | 225 |
| abstract_inverted_index.understood. | 252 |
| abstract_inverted_index.variational | 83 |
| abstract_inverted_index.constraints, | 59 |
| abstract_inverted_index.constraints. | 123 |
| abstract_inverted_index.conventional | 82 |
| abstract_inverted_index.entanglement | 150, 155 |
| abstract_inverted_index.observables, | 15 |
| abstract_inverted_index.two-particle | 154 |
| abstract_inverted_index.complementary | 80 |
| abstract_inverted_index.half-filling. | 176 |
| abstract_inverted_index.topologically | 191 |
| abstract_inverted_index.wavefunction. | 68 |
| abstract_inverted_index.diagonalization | 109 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 5 |
| citation_normalized_percentile |