In this work, we present a novel representation of matrix product states (MPS) within the framework of quasi-local algebras. By introducing an enhanced compatibility condition, we enable the extension of finite MPS to an infinite-volume state, providing new insights into complex, high-dimensional quantum systems. As an illustrative example, we apply this method to the Greenberger-Horne-Zeilinger (GHZ) state. This approach offers significant potential for advancing theoretical frameworks and practical methodologies in the field of quantum information.
@article{arxiv.2411.04149,
title = {Matrix Product States in Quantum Spin Chains},
author = {Abdessatar Souissi and Amenallah Andolsi},
journal= {arXiv preprint arXiv:2411.04149},
year = {2024}
}