Internal structure of gauge-invariant Projected Entangled Pair States

TL;DR

This paper investigates the internal structure of gauge-invariant PEPS, revealing how local gauge symmetries influence tensor properties in higher-dimensional lattice models, advancing the understanding of non-perturbative gauge theories.

Contribution

It provides the first detailed analysis of how gauge symmetries shape the internal tensor structure of PEPS in higher dimensions, extending previous global symmetry results.

Findings

Characterization of gauge-invariant PEPS tensor structure

Extension of symmetry-structure connection to gauge symmetries

Framework applicable to arbitrary graphs for lattice gauge theories

Abstract

Projected entangled pair states (PEPS) are very useful in the description of strongly correlated systems, partly because they allow encoding symmetries, either global or local (gauge), naturally. In recent years, PEPS with local symmetries have increasingly been used in the study of non-perturbative regimes of lattice gauge theories, most prominently as a way to construct variational ansatz states depending only on a small number of parameters and yet capturing the relevant physical properties. For the case of one-dimensional PEPS (Matrix Product States - MPS) a bidirectional connection was established between the internal structure of the tensor network, i.e. the mathematical properties of the constituent tensors, and the symmetry. In higher dimensions this has only been done for global symmetries, where in the local (gauge) case it is known only how to construct gauge-invariant states, but not what the symmetry implies on the internal structure of the PEPS. In the present work we complete this missing piece and study the internal structure of projected entangled pair states with a gauge symmetry. The PEPS we consider consist of matter and gauge field tensors placed on the vertices and edges, respectively, of arbitrary graphs.