Simple Hamiltonians for Matrix Product State models

Norbert Schuch, András Molnár, David Perez-Garcia

Publications: Working paperPreprint

Abstract

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.
Original languageEnglish
PublisherarXiv
Pages1-6
DOIs
Publication statusPublished - 13 Mar 2025

Austrian Fields of Science 2012

  • 103025 Quantum mechanics
  • 101028 Mathematical modelling
  • 103036 Theoretical physics

Fingerprint

Dive into the research topics of 'Simple Hamiltonians for Matrix Product State models'. Together they form a unique fingerprint.

Cite this