# Examples of symmetry-preserving truncations in tensor field theory

## TL;DR

This paper demonstrates that symmetry-preserving tensor truncations can accurately reproduce the universal properties of the non-linear O(2) sigma model and the Abelian Higgs model, facilitating quantum simulations.

## Contribution

It introduces symmetry-compatible tensor truncations for lattice models, enabling simplified formulations suitable for quantum computing and simulations.

## Key findings

- Tensor truncations preserve model symmetries.
- Universal properties are maintained with simplified models.
- Extensions to non-Abelian symmetries and fermionic models are discussed.

## 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.