Speaker
Description
Tensor networks offer a sign-problem-free framework for studying lattice field theories, provide direct access to partition functions, free energies, and correlation functions through controlled, deterministic approximations. This introductory talk aims to bridge the gap for the lattice community by presenting the essential concepts and computational tools of the tensor network approach.
I will begin with a pedagogical introduction to tensor networks and the role of entanglement in their efficiency. I will then show how the Euclidean path integral of a lattice model maps exactly onto a tensor network: by locally factorising the Boltzmann weights, the partition function becomes the contraction of a translationally invariant network of local tensors, illustrated with both spin models and gauge theories.
Finally, I will survey methods for evaluating these networks, focusing on coarse-graining methods refereed to as Tensor Network Renormalisation, and the challenges of reaching higher dimensions and continuous gauge groups.