Entanglement membrane in exactly solvable lattice models

Michael A. Rampp, Suhail A. Rather, Pieter W. Claeys
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Abstract

Entanglement membrane theory is an effective coarse-grained description of entanglement dynamics and operator growth in chaotic quantum many-body systems. The fundamental quantity characterizing the membrane is the entanglement line tension. However, determining the entanglement line tension for microscopic models is in general exponentially difficult. We compute the entanglement line tension in a recently introduced class of exactly solvable yet chaotic unitary circuits, so-called generalized dual-unitary circuits, obtaining a nontrivial form that gives rise to a hierarchy of velocity scales with vE<vB. For the lowest level of the hierarchy, L¯2 circuits, the entanglement line tension can be computed entirely, while for the higher levels the solvability is reduced to certain regions in spacetime. This partial solvability enables us to place bounds on the entanglement velocity. We find that L¯2 circuits saturate certain bounds on entanglement growth that are also saturated in holographic models. Furthermore, we relate the entanglement line tension to temporal entanglement and correlation functions. We also develop methods of constructing generalized dual-unitary gates, including constructions based on complex Hadamard matrices that exhibit additional solvability properties and constructions that display behavior unique to local dimension greater than or equal to three. Our results shed light on entanglement membrane theory in microscopic Floquet lattice models and enable us to perform nontrivial checks on the validity of its predictions by comparison to exact and numerical calculations. Moreover, they demonstrate that generalized dual-unitary circuits display a more generic form of information dynamics than dual-unitary circuits.

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精确可解晶格模型中的纠缠膜
纠缠膜理论是对混沌量子多体系统中纠缠动力学和算子增长的有效粗粒度描述。表征膜的基本量是纠缠线张力。然而,确定微观模型的纠缠线张力一般都是指数级的困难。我们计算了最近引入的一类精确可解但混乱的单元电路(即所谓的广义双单元电路)中的纠缠线张力,得到了一种非微观形式,它产生了一个速度尺度为 vE<vB 的层次结构。对于层次结构的最底层,即 L¯2 电路,纠缠线张力可以完全计算出来,而对于更高层次的电路,可解性则被降低到时空中的某些区域。这种部分可解性使我们能够确定纠缠速度的边界。我们发现,L¯2 电路使纠缠增长的某些界限达到饱和,而这些界限在全息模型中也是饱和的。此外,我们还将纠缠线张力与时间纠缠和相关函数联系起来。我们还开发了构建广义二元统一门的方法,包括基于复杂哈达玛矩阵的构建,这种构建表现出额外的可解性,并显示出局部维度大于或等于三的独特行为。我们的结果揭示了微观浮凸晶格模型中的纠缠膜理论,并使我们能够通过与精确计算和数值计算的比较,对其预测的有效性进行非微观检查。此外,它们还证明了广义双单元电路比双单元电路显示出更通用的信息动力学形式。
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CiteScore
8.60
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