Extracting Higher Central Charge from a Single Wave Function Article Swipe
Ryohei Kobayashi
,
Taige Wang
,
Tomohiro Soejima
,
Roger S. K. Mong
,
Shinsei Ryu
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1103/physrevlett.132.016602
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1103/physrevlett.132.016602
A (2+1)D topologically ordered phase may or may not have a gappable edge, even if its chiral central charge c_ is vanishing. Recently, it was discovered that a quantity regarded as a "higher" version of chiral central charge gives a further obstruction beyond c_ to gapping out the edge. Here, in this Letter, we show that the higher central charges can be characterized by the expectation value of the partial rotation operator acting on the wave function of the topologically ordered state. This allows us to extract the higher central charge from a single wave function, which can be evaluated on a quantum computer. Our characterization of the higher central charge is analytically derived from the modular properties of edge conformal field theory, as well as the numerical results with the ν = 1/2 bosonic Laughlin state and the non-Abelian gapped phase of the Kitaev honeycomb model, which corresponds to U(1)2 and Ising topological order, respectively. The Letter establishes a numerical method to obtain a set of obstructions to the gappable edge of (2+1)D bosonic topological order beyond c_, which enables us to completely determine if a (2+1)D bosonic Abelian topological order has a gappable edge or not. We also point out that the expectation values of the partial rotation on a single wave function put a constraint on the low-energy spectrum of the bulk-boundary system of (2+1)D bosonic topological order, reminiscent of the Lieb-Schultz-Mattis-type theorems.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1103/physrevlett.132.016602
- OA Status
- gold
- Cited By
- 14
- References
- 43
- Related Works
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- OpenAlex ID
- https://openalex.org/W4390579938
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https://openalex.org/W4390579938Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1103/physrevlett.132.016602Digital Object Identifier
- Title
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Extracting Higher Central Charge from a Single Wave FunctionWork title
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2024Year of publication
- Publication date
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2024-01-04Full publication date if available
- Authors
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Ryohei Kobayashi, Taige Wang, Tomohiro Soejima, Roger S. K. Mong, Shinsei RyuList of authors in order
- Landing page
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https://doi.org/10.1103/physrevlett.132.016602Publisher landing page
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YesWhether a free full text is available
- OA status
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goldOpen access status per OpenAlex
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https://escholarship.org/uc/item/1hm625h6Direct OA link when available
- Concepts
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Physics, Central charge, Charge (physics), Order (exchange), Wave function, Quantum mechanics, Mathematical physics, Topology (electrical circuits), Conformal map, Combinatorics, Mathematical analysis, Mathematics, Finance, EconomicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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14Total citation count in OpenAlex
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2025: 9, 2024: 4, 2023: 1Per-year citation counts (last 5 years)
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10Other works algorithmically related by OpenAlex
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