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arXiv · 2504.02815

Logarithmic entanglement lightcone from eigenstate correlations in the many-body localised phase

Ratul Thakur·Bikram Pain·Sthitadhi Roy
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Abstract

We investigate the operator entanglement of the time-evolution operator through the framework of eigenstate correlations. Focusing on strongly disordered quantum many-body systems in the many-body localised (MBL) regime, we analyse the operator entanglement across various spatiotemporal cuts, revealing the logarithmic lightcone of entanglement spreading. We demonstrate that this logarithmic lightcone arises directly from a hierarchy of energyscales and lengthscales encoded in eigenstate correlations. By characterising the statistics of these hierarchical scales, we develop a microscopic theory for the spatiotemporal structure of entanglement spreading in MBL systems -- without invoking phenomenological constructs such as $\ell$-bits. This approach reveals the fundamental connection between eigenstate correlations and the emergent entanglement structure in MBL systems.

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Ratul Thakur, Bikram Pain, Sthitadhi Roy. 2025-04-03. Logarithmic entanglement lightcone from eigenstate correlations in the many-body localised phase. https://doi.org/10.1103/physrevb.111.174206

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