Entanglement entropy in the ground state of non-interacting massless Dirac fermions in dimension one
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917636288282624 |
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| author | Ferro, Fabrizio Pfeiffer, Paul Spitzer, Wolfgang |
| author_facet | Ferro, Fabrizio Pfeiffer, Paul Spitzer, Wolfgang |
| contents | We present a novel proof of a formula of Casini and Huerta for the entanglement entropy of the ground state of non-interacting massless Dirac fermions in dimension one localized to (a union of) intervals and generalize it to the case of Rényi entropies. At first, we prove that these entropies are well-defined for non-intersecting intervals. This is accomplished by an inequality of Alexander V.~Sobolev. Then we compute this entropy using a trace formula for Wiener--Hopf operators by Harold Widom. For intersecting intervals, we discuss an extended entropy formula of Casini and Huerta and support this with a proof for polynomial test functions (instead of entropy). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07068 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Entanglement entropy in the ground state of non-interacting massless Dirac fermions in dimension one Ferro, Fabrizio Pfeiffer, Paul Spitzer, Wolfgang Mathematical Physics We present a novel proof of a formula of Casini and Huerta for the entanglement entropy of the ground state of non-interacting massless Dirac fermions in dimension one localized to (a union of) intervals and generalize it to the case of Rényi entropies. At first, we prove that these entropies are well-defined for non-intersecting intervals. This is accomplished by an inequality of Alexander V.~Sobolev. Then we compute this entropy using a trace formula for Wiener--Hopf operators by Harold Widom. For intersecting intervals, we discuss an extended entropy formula of Casini and Huerta and support this with a proof for polynomial test functions (instead of entropy). |
| title | Entanglement entropy in the ground state of non-interacting massless Dirac fermions in dimension one |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2404.07068 |