Simple Hamiltonians for Matrix Product State models

Autor(en)

Norbert Schuch, András Molnár, David Perez-Garcia

Abstrakt

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.

Organisation(en)

Institut für Mathematik, Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

Universidad Complutense De Madrid, Spanish National Research Council (CSIC)

Seiten

1-6

DOI

https://doi.org/10.48550/arXiv.2503.10767

Publikationsdatum

03-2025

ÖFOS 2012

103025 Quantenmechanik, 101028 Mathematische Modellierung, 103036 Theoretische Physik

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/ef74afe9-8e39-4a5e-bd99-f85c7f27d754