Non-abelian symmetries in the ITensor software library

Tensor network methods are a set of numerical algorithms designed to study strongly correlated systems in condensed matter and high energy physics. They aim to construct efficient low-rank approximations of high dimensional objects such as quantum wavefunctions and produce state of the art results in many-body physics. ITensors.jl is a Julia library dedicated to tensor network computations. It is designed to provide easy access to powerful tensor network algorithms with a high level interface accessible to non experts.

As many physical systems of interest exhibit symmetries, such as translation invariance or SU(2) spin symmetry, it is natural to make use of these symmetries inside tensor networks algorithm. Indeed, they can be encoded directly at the level of the tensor in order to enforce constraints on the ansatz as well as to dramatically improve performances. Implementing abelian symmetries is relatively straightforward and already available in ITensor or other tensor libraries, however a generic implementation of non-abelian symmetries is much more challenging. It requires to define a complex internal structure for each tensor as well as the tools needed to modify this internal structure.

In this talk, we detail the algorithms used to encode non-abelian symmetries in tensor networks and discuss their implementation in the ITensors.jl software library.