Matrix Product States (MPS) and Tensor Networks provide a general framework for the construction of solvable models. The best-known example is the Affleck-Kennedy-Lieb-Tasaki (AKLT) model, which is the ground state of a 2-body nearest-neighbor parent Hamiltonian. We show that such simple parent Hamiltonians for MPS models are, in fact, much more prevalent than hitherto known: The existence of a single example with a simple Hamiltonian for a given choice of dimensions already implies that any generic MPS with those dimensions possesses an equally simple Hamiltonian. We illustrate our finding by discussing a number of models with nearest-neighbor parent Hamiltonians, which generalize the AKLT model on various levels.
Cite
@article{arxiv.2503.10767,
title = {Simple Hamiltonians for Matrix Product State models},
author = {Norbert Schuch and Andras Molnar and David Perez-Garcia},
journal= {arXiv preprint arXiv:2503.10767},
year = {2025}
}