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

• URL: http://arxiv.org/abs/2504.02815v1
• Date: Thu, 03 Apr 2025 17:57:10 GMT
• Title: Logarithmic entanglement lightcone from eigenstate correlations in the many-body localised phase
• Authors: Ratul Thakur, Bikram Pain, Sthitadhi Roy,
• Abstract summary: We investigate the operator entanglement of the time-evolution operator through the framework of eigenstate correlations.<n>This approach reveals the fundamental connection between eigenstate correlations and the emergent entanglement structure in MBL systems.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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