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arXiv · 2410.19541

The product structure of MPS-under-permutations

Marta Florido-Llinàs·Álvaro M. Alhambra·Rahul Trivedi·Norbert Schuch·David Pérez-García·J. Ignacio Cirac
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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.

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Marta Florido-Llinàs, Álvaro M. Alhambra, Rahul Trivedi, Norbert Schuch, David Pérez-García, J. Ignacio Cirac. 2024-10-25. The product structure of MPS-under-permutations. https://doi.org/10.1103/8sbs-t24w

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