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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 language | English |
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Publisher | arXiv |
Pages | 1-6 |
DOIs | |
Publication status | Published - 13 Mar 2025 |
Austrian Fields of Science 2012
- 103025 Quantum mechanics
- 101028 Mathematical modelling
- 103036 Theoretical physics
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Dive into the research topics of 'Simple Hamiltonians for Matrix Product State models'. Together they form a unique fingerprint.Projects
- 4 Active
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quantA: Quantum Science Austria
Aspelmeyer, M., Arndt, M., Brukner, C., Schuch, N., Walther, P. & Nunnenkamp, A.
1/10/23 → 30/09/28
Project: Research funding
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