Normal projected entangled pair states generating the same state

TL;DR

This paper investigates the equivalence of different tensor sets generating the same quantum state in projected entangled-pair states (PEPS), extending understanding from 1D to higher dimensions for normal tensors.

Contribution

It provides a comprehensive analysis of the relations between tensor sets in PEPS across all dimensions, focusing on the class of normal tensors.

Findings

Different tensor sets can generate the same PEPS state.

The relation between tensor sets is characterized for normal tensors in any dimension.

Results have implications for understanding symmetries and phases in quantum many-body systems.

Abstract

Tensor networks are generated by a set of small rank tensors and define many-body quantum states in a succinct form. The corresponding map is not one-to-one: different sets of tensors may generate the very same state. A fundamental question in the study of tensor networks naturally arises: what is then the relation between those sets? The answer to this question in one dimensional setups has found several applications, like the characterization of local and global symmetries, the classification of phases of matter and unitary evolutions, or the determination of the fixed points of renormalization procedures. Here we answer this question for projected entangled-pair states (PEPS) in any dimension and lattice geometry, as long as the tensors generating the states are normal, which constitute an important and generic class.