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arXiv · 2512.04179

Entanglement membrane in the Brownian SYK chain

Márk Mezei·Harshit Rajgadia
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Abstract

There is mounting evidence that entanglement dynamics in chaotic many-body quantum systems in the limit of large subsystems and long times is described by an entanglement membrane effective theory. In this paper, we derive the membrane description in a solvable chaotic large-$N$ model, the Brownian SYK chain. This model has a collective field description in terms of fermion bilinears connecting different folds of the multifold Schwinger-Keldysh path integral used to compute R\'enyi entropies. The entanglement membrane is a traveling wave solution of the saddle point equations governing these collective fields. The entanglement membrane is characterised by a velocity $v$ and a membrane tension ${\cal E}(v)$ that we calculate. We find that the membrane has finite width for $v v_B$, the membrane splits into two wave fronts, each moving with the butterfly velocity. Our results provide a new viewpoint on the entanglement membrane and uncover new connections between quantum information dynamics and scrambling.

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Márk Mezei, Harshit Rajgadia. 2025-12-03. Entanglement membrane in the Brownian SYK chain. https://arxiv.org/abs/2512.04179

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