2025-07-24 –, Main Room 6
Tensor network methods are a set of numerical algorithms designed to study strongly correlated systems in quantum physics. ITensors.jl is a high performance library providing easy access to them. As many physical models exhibit symmetries such as SU(2), enforcing them directly within the tensors leads to significant performance gains. In this talk, we introduce the core concepts of tensor networks, the basics of ITensor and expose its implementation of non-abelian symmetries.
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.
Using the framework of representation theory, every leg in the tensor network is associated with a representation of a given symmetry group G. A symmetric tensor is defined as a tensor invariant under the action of a G on each of its legs. Such a constraint on a tensor allows for a decomposition between a multiplicity part and a structural part. The latter is entirely determined by the group and allows one to store and manipulate the multiplicity part only without any loss of information, leading to significant performance gains.
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.
Olivier Gauthé is an Associate Data Scientist at the Center for Computational Quantum Physics (CCQ) of the Flatiron Institute in New York City. Before moving to CCQ, he obtained a physics PhD in France at Toulouse III University and then joined EPFL in Lausanne, Switzerland as a postdoctoral researcher. He is working on numerical methods to study strongly correlated systems in condensed matter physics, with a focus on tensor network algorithms and 2D spin systems.