MPS Stability and the Intersection Property

José Garre Rubio; Alex Turzillo; András Molnár

doi:10.48550/arXiv.2501.17109

MPS Stability and the Intersection Property

José Garre Rubio
, Alex Turzillo
, András Molnár

Department of Mathematics

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

We identify a property of the local tensors of matrix product states (MPS) that guarantees that their parent Hamiltonians satisfy the intersection property. The intersection property ensures that the ground space consists of MPS, with degeneracy bounded by the square of the bond dimension. The new local property, dubbed stability, generalizes (block) injectivity and is satisfied by the MPS tensors that construct the W state, domain wall superposition states, and their generalizations.

Original language	English
Number of pages	23
Journal	Annales Henri Poincare
DOIs	https://doi.org/10.48550/arXiv.2501.17109 https://doi.org/10.1007/s00023-025-01650-3
Publication status	Published - 2 Dec 2025

Funding

Funders	Funder number
Fonds zur Förderung der wissenschaftlichen Forschung (FWF)	10.55776/J4796

Austrian Fields of Science 2012

101028 Mathematical modelling
103025 Quantum mechanics
103036 Theoretical physics

Access to Document

10.48550/arXiv.2501.17109Licence: Unspecified
10.1007/s00023-025-01650-3Licence: CC BY 4.0

SEQUAM: Symmetries and Entanglement in Quantum Matter
Schuch, N. (Project Lead)
1/10/20 → 30/09/26
Project: Research funding

Cite this

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abstract = "We identify a property of the local tensors of matrix product states (MPS) that guarantees that their parent Hamiltonians satisfy the intersection property. The intersection property ensures that the ground space consists of MPS, with degeneracy bounded by the square of the bond dimension. The new local property, dubbed stability, generalizes (block) injectivity and is satisfied by the MPS tensors that construct the W state, domain wall superposition states, and their generalizations.",

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AU - Turzillo, Alex

AU - Molnár, András

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AB - We identify a property of the local tensors of matrix product states (MPS) that guarantees that their parent Hamiltonians satisfy the intersection property. The intersection property ensures that the ground space consists of MPS, with degeneracy bounded by the square of the bond dimension. The new local property, dubbed stability, generalizes (block) injectivity and is satisfied by the MPS tensors that construct the W state, domain wall superposition states, and their generalizations.

U2 - 10.48550/arXiv.2501.17109

DO - 10.48550/arXiv.2501.17109

M3 - Article

SN - 1424-0637

JO - Annales Henri Poincare

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ER -

MPS Stability and the Intersection Property

Abstract

Funding

Austrian Fields of Science 2012

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Projects

SEQUAM: Symmetries and Entanglement in Quantum Matter

Cite this