MPS Stability and the Intersection Property

05.12.2025

Out now in Annales Henri Poincaré: A new condition on matrix product states – dubbed stability – extends injectivity and guarantees well-controlled parent Hamiltonian ground spaces, covering paradigmatic examples such as W, Dicke, and domain-wall superposition states.

Congratulations to José Garre-Rubio, Alex Turzillo, and András Molnár on the publication of their work "MPS Stability and the Intersection Property" in Annales Henri Poincaré (2025). 

To find out more about this paper, check out the abstract below and read the open-access article in the 'online first' section of Annales Henri Poincaré [DOI: 10.1007/s00023-025-01650-3].

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.

This work has received support through the ERC grant SEQUAM and the Austrian Science Fund FWF (grant DOI 10.55776/J4796).

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