Dual-isometric Projected Entangled Pair States

TL;DR

This paper introduces a new class of Project Entangled Pair States with dual isometric constraints, enabling efficient calculation of local observables and correlation functions while maintaining rich physical properties.

Contribution

The paper proposes a novel dual-isometric PEPS framework that improves computational tractability and retains essential physical features, including universal quantum computation encoding.

Findings

Enables efficient calculation of local observables and two-point correlations.

Can encode universal quantum computations.

Represents a transition from topological to trivial order.

Abstract

Efficient characterization of higher dimensional many-body physical states presents significant challenges. In this paper, we propose a new class of Project Entangled Pair State (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 computations and can represent a transition from topological to trivial order.