Decorated tensor network renormalization for lattice gauge theories and spin foam models

TL;DR

This paper introduces decorated tensor network techniques to efficiently coarse grain lattice gauge theories, explicitly preserving gauge symmetry and enabling direct access to physical observables.

Contribution

It proposes a novel decorated tensor network approach that maintains gauge invariance during coarse graining for lattice gauge theories and related models.

Findings

Successfully applied to models with finite Abelian groups

Preserves gauge symmetry explicitly during coarse graining

Allows direct computation of expectation values and correlations

Abstract

Tensor network techniques have proved to be powerful tools that can be employed to explore the large scale dynamics of lattice systems. Nonetheless, the redundancy of degrees of freedom in lattice gauge theories (and related models) poses a challenge for standard tensor network algorithms. We accommodate for such systems by introducing an additional structure decorating the tensor network. This allows to explicitly preserve the gauge symmetry of the system under coarse graining and straightforwardly interpret the fixed point tensors. We propose and test (for models with finite Abelian groups) a coarse graining algorithm for lattice gauge theories based on decorated tensor networks. We also point out that decorated tensor networks are applicable to other models as well, where they provide the advantage to give immediate access to certain expectation values and correlation functions.