Continuum mechanics of entanglement in noisy interacting fermion chains
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917230652948480 |
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| author | Swann, Tobias Nahum, Adam |
| author_facet | Swann, Tobias Nahum, Adam |
| contents | We develop an effective continuum description for information scrambling in a chain of randomly interacting Majorana fermions. The approach is based on the semiclassical treatment of the path integral for an effective spin chain that describes "two-replica" observables such as the entanglement purity and the OTOC. This formalism gives exact results for the entanglement membrane and for operator spreading in the limit of weak interactions. In this limit there is a large crossover lengthscale between free and interacting behavior, and this large lengthscale allows for a continuum limit and a controlled saddle-point calculation. The formalism is also somewhat different from that known from random unitary circuits. The entanglement membrane emerges as a kind of bound state of two travelling waves, and shows an interesting unbinding phenomenon as the velocity of the entanglement membrane approaches the butterfly velocity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_21134 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Continuum mechanics of entanglement in noisy interacting fermion chains Swann, Tobias Nahum, Adam Statistical Mechanics Disordered Systems and Neural Networks Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics We develop an effective continuum description for information scrambling in a chain of randomly interacting Majorana fermions. The approach is based on the semiclassical treatment of the path integral for an effective spin chain that describes "two-replica" observables such as the entanglement purity and the OTOC. This formalism gives exact results for the entanglement membrane and for operator spreading in the limit of weak interactions. In this limit there is a large crossover lengthscale between free and interacting behavior, and this large lengthscale allows for a continuum limit and a controlled saddle-point calculation. The formalism is also somewhat different from that known from random unitary circuits. The entanglement membrane emerges as a kind of bound state of two travelling waves, and shows an interesting unbinding phenomenon as the velocity of the entanglement membrane approaches the butterfly velocity. |
| title | Continuum mechanics of entanglement in noisy interacting fermion chains |
| topic | Statistical Mechanics Disordered Systems and Neural Networks Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2601.21134 |