从对偶酉到双酉：一个用于精确可解多体量子动力学的2-范畴模型
From dual-unitary to biunitary: a 2-categorical model for exactly-solvable many-body quantum dynamics
AI总结：
提出一个2-范畴框架，将对偶酉砖块电路与钟表电路统一推广为广义异构双酉电路，证明其保持精确可解性及因果光锥上单点关联等特征，并实现最大纠缠增长与精确热化。
摘要：
对偶酉砖块电路是用于多体混沌量子系统的精确可解模型，基于在时间和空间方向上均为酉的2-位点门。Prosen最近描述了一种称为“面周相互作用对偶酉”的替代模型，我们在此称之为“钟表结构”，它基于以非砖块结构组合的2-受控1-位点酉算符，但具有许多相同的诱人全局性质。我们提出了一个2-范畴框架，同时推广了这两个现有模型，并用它证明了砖块和钟表电路可以丰富地相互作用，产生新型广义异构电路。我们证明这些相互作用由量子组合数据控制，并对其进行了精确刻画。这些广义电路保持精确可解，并且我们证明它们保留了原始模型的诱人特征，例如单点关联函数除在因果光锥上外处处为零。我们提出的框架允许我们将可解初态的概念直接扩展到这些双酉电路，并证明在双酉电路动力学下，经过有限时间步后会导致最大纠缠增长和精确热化。
英文摘要：
Dual-unitary brickwork circuits are an exactly-solvable model for many-body chaotic quantum systems, based on 2-site gates which are unitary in both the time and space directions. Prosen has recently described an alternative model called 'dual-unitary interactions round-a-face', which we here call 'clockwork', based on 2-controlled 1-site unitaries composed in a non-brickwork structure, yet with many of the same attractive global properties. We present a 2-categorical framework that simultaneously generalizes these two existing models, and use it to show that brickwork and clockwork circuits can interact richly, yielding new types of generalized heterogeneous circuits. We show that these interactions are governed by quantum combinatorial data, which we precisely characterize. These generalized circuits remain exactly-solvable and we show that they retain the attractive features of the original models such as single-site correlation functions vanishing everywhere except on the causal light-cone. Our presented framework allows us to directly extend the notion of solvable initial states to these biunitary circuits, which are shown to result in maximal entanglement growth and exact thermalization after finitely many time steps under biunitary circuit dynamics.
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