Dual-Isometric Projected Entangled Pair States.

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.