Examples of symmetry-preserving truncations in tensor field theory

Abstract: We consider the tensor formulation of the non-linear O(2) sigma model and its gauged version (the compact Abelian Higgs model), on a $D$-dimensional cubic lattice, and show that tensorial truncations are compatible with the general identities derived from the symmetries of these models. This means that the universal properties of these models can be reproduced with highly simplified formulations desirable for implementations with quantum computers or for quantum simulations experiments. We briefly discuss the extensions to non-Abelian symmetries and models with fermions.