Entanglement in interacting Majorana chains and transitions of von Neumann algebras
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914101205139456 |
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| author | Basteiro, Pablo Di Giulio, Giuseppe Erdmenger, Johanna Xian, Zhuo-Yu |
| author_facet | Basteiro, Pablo Di Giulio, Giuseppe Erdmenger, Johanna Xian, Zhuo-Yu |
| contents | We consider Majorana lattices with two-site interactions consisting of a general function of the fermion bilinear. The models are exactly solvable in the limit of a large number of on-site fermions. The four-site chain exhibits a quantum phase transition controlled by the hopping parameters and manifests itself in a discontinuous entanglement entropy, obtained by constraining the one-sided modular Hamiltonian. Inspired by recent work within the AdS/CFT correspondence, we identify transitions between types of von Neumann operator algebras throughout the phase diagram. We find transitions of the form II$_1\leftrightarrow\,$III$\,\,\leftrightarrow\,\,$I$_\infty$ that reduce to II$_1\leftrightarrow\,\,$I$_\infty$ in the strongly interacting limit, where they connect non-factorized and factorized ground states. Our results provide novel realizations of such transitions in a controlled many-body model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04764 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Entanglement in interacting Majorana chains and transitions of von Neumann algebras Basteiro, Pablo Di Giulio, Giuseppe Erdmenger, Johanna Xian, Zhuo-Yu High Energy Physics - Theory Statistical Mechanics Quantum Physics We consider Majorana lattices with two-site interactions consisting of a general function of the fermion bilinear. The models are exactly solvable in the limit of a large number of on-site fermions. The four-site chain exhibits a quantum phase transition controlled by the hopping parameters and manifests itself in a discontinuous entanglement entropy, obtained by constraining the one-sided modular Hamiltonian. Inspired by recent work within the AdS/CFT correspondence, we identify transitions between types of von Neumann operator algebras throughout the phase diagram. We find transitions of the form II$_1\leftrightarrow\,$III$\,\,\leftrightarrow\,\,$I$_\infty$ that reduce to II$_1\leftrightarrow\,\,$I$_\infty$ in the strongly interacting limit, where they connect non-factorized and factorized ground states. Our results provide novel realizations of such transitions in a controlled many-body model. |
| title | Entanglement in interacting Majorana chains and transitions of von Neumann algebras |
| topic | High Energy Physics - Theory Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2401.04764 |