Bibliometric Analysis and Overview of Matrix Product States in the Bose-Hubbard Model - Gómez, Juan Sebastián; Rodríguez , Karen Cecilia (Ingeniería, 2025)
Context: Quantum many-body systems have been a prominent topic over the past two decades, underpinning advancements in superconductors, ultracold atoms, and quantum computing, among other fields. This bibliometric analysis explores key concepts, influential authors, and the current significance of a powerful family of algorithms in computational physics, i.e., density matrix renormalization group (DMRG) algorithms. Special emphasis is placed on the use of tensor product states in developing classical simulations of quantum systems. Method: This paper presents a literature review sourced from the SCOPUS database. It analyzes trends and approaches related to uncertainty in numerical developments for quantum many-body systems, with a focus on the Bose-Hubbard Model, in order to better understand the imposition of additional constraints to ensure the validity of the results. Results: The increasing number of publications on this topic over the last decade indicates a growing interest in solutions for many-body quantum systems, driven by promising advances in superconductive materials, quantum computing, and other impactful areas. Conclusions: This work explored essential foundational works to help beginners understand a well-established technique that aims to overcome the limitations of classical computing. The use of matrix product states in DMRG algorithms is gaining significant traction in various fields, including quantum computing, machine learning, and statistical mechanics, with the purpose of addressing the challenges related to quantum many-body systems.