Efficient characterization of higher dimensional many-body physical states presents significant challenges. In this Letter, we propose a new class of projected entangled pair states (PEPS) that incorporates two isometric conditions. This new class facilitates the efficient calculation of general local observables and certain two-point correlation functions, which have been previously shown to be intractable for general PEPS, or PEPS with only a single isometric constraint. Despite incorporating two isometric conditions, our class preserves the rich physical structure while enhancing the analytical capabilities. It features a large set of tunable parameters, with only a subleading correction compared to that of general PEPS. Furthermore, we analytically demonstrate that this class can encode universal quantum computation and can represent a transition from topological to trivial order.

中文翻译：

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双等轴测投影纠缠对状态


高效表征高维多体物理状态带来了重大挑战。在这封信中，我们提出了一类新的投影纠缠对态 （PEPS），其中包含两个等距条件。这个新类有助于有效计算一般局部可观察对象和某些两点相关函数，这些函数之前已被证明对于一般 PEPS 或只有一个等距约束的 PEPS 来说是棘手的。尽管包含两个等距条件，我们的类在增强分析能力的同时保留了丰富的物理结构。它具有大量可调参数，与一般 PEPS 相比，只有次导校正。此外，我们分析证明，此类可以编码通用量子计算，并且可以表示从拓扑到平凡顺序的转变。