MPS Stability and the Intersection Property
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.
Authors
- José Garre-Rubio (ORCID: https://orcid.org/0000-0003-1845-7554)
- András Molnár
- Alex Turzillo
Institutions
- University of Vienna (AT)
- Perimeter Institute (CA)
- Instituto de Investigación en Ciencias de la Alimentación (ES)
- Universidad Autónoma de Madrid (ES)
Publication Details
- Journal
- Annales Henri Poincaré
- Published
- 2025-12-02
- DOI
- https://doi.org/10.1007/s00023-025-01650-3
- Primary Topic
- Algebraic structures and combinatorial models
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Government of Canada
- European Commission
- Austrian Science Fund
- Institut Périmètre de physique théorique
- Ministry of Colleges and Universities