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Abstract

This paper is a manual with tips and tricks for programming tensor network
algorithms with global $SU(2)$ symmetry. We focus on practical details that are
many times overlooked when it comes to implementing the basic building blocks
of codes, such as useful data structures to store the tensors, practical ways
of manipulating them, and so forth. Here we do not restrict ourselves to any
specific tensor network method, but keep always in mind that the implementation
should scale well for simulations of higher-dimensional systems using, e.g.,
Projected Entangled Pair States, where tensors with many indices may show up.
To this end, the structural tensors (or intertwiners) that arise in the usual
decomposition of $SU(2)$-symmetric tensors are never explicitly stored
throughout the simulation. Instead, we store and manipulate the corresponding
fusion trees - an algebraic specification of the symmetry constraints on the
tensor - in order to implement basic $SU(2)$-symmetric tensor operations.