The product structure of MPS-under-permutations
Abstract
Tensor network methods have proved to be highly effective in addressing a wide variety of physical scenarios, including those lacking an intrinsic one-dimensional geometry. In such contexts, it is possible for the problem to exhibit a weak form of permutational symmetry, in the sense that entanglement behaves similarly across any arbitrary bipartition. In this paper, we show that translationally-invariant (TI) matrix product states (MPS) with this property are trivial, meaning that they are either product states or superpositions of a few of them. The results also apply to non-TI generic MPS, as well as further relevant examples of MPS including the W state and the Dicke states in an approximate sense. Our findings motivate the usage of ans\"atze simpler than tensor networks in systems whose structure is invariant under permutations.
Cite
@article{arxiv.2410.19541,
title = {The product structure of MPS-under-permutations},
author = {Marta Florido-Llinàs and Álvaro M. Alhambra and Rahul Trivedi and Norbert Schuch and David Pérez-García and J. Ignacio Cirac},
journal= {arXiv preprint arXiv:2410.19541},
year = {2026}
}
Comments
18 pages