<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0121-750X</journal-id>
<journal-title><![CDATA[Ingeniería]]></journal-title>
<abbrev-journal-title><![CDATA[ing.]]></abbrev-journal-title>
<issn>0121-750X</issn>
<publisher>
<publisher-name><![CDATA[Universidad Distrital Francisco José de Caldas]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0121-750X2025000100009</article-id>
<article-id pub-id-type="doi">10.14483/23448393.22292</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Bibliometric Analysis and Overview of Matrix Product States in the Bose-Hubbard Model]]></article-title>
<article-title xml:lang="es"><![CDATA[Estudio bibliométrico y revisión del uso de estados producto de matrices en el modelo de Bose-Hubbard]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Gómez]]></surname>
<given-names><![CDATA[Juan Sebastián]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Rodríguez]]></surname>
<given-names><![CDATA[Karen]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad del Valle  ]]></institution>
<addr-line><![CDATA[Cali ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>04</month>
<year>2025</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>04</month>
<year>2025</year>
</pub-date>
<volume>30</volume>
<numero>1</numero>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0121-750X2025000100009&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0121-750X2025000100009&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0121-750X2025000100009&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract  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.  Acknowledgments: This work was supported by Universidad del Valle under internal project CI. 71344.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen  Contexto: Los sistemas cuánticos de muchos cuerpos han sido un tema prominente durante las últimas dos décadas, sustentando avances en superconductores, átomos ultrafríos y computación cuántica. Este análisis bibliométrico explora conceptos clave, autores influyentes y la significancia actual de una poderosa familia de algoritmos en física computacional, i.e., los algoritmos del grupo de renormalización de matriz de densidad (DMRG). Se pone un énfasis especial en el uso de estados producto de tensor en el desarrollo de simulaciones clásicas de sistemas cuánticos.  Métodos: Este artículo presenta una revisión de la literatura obtenida de la base de datos de SCOPUS. Analiza tendencias y enfoques relacionados con el concepto de incertidumbre dentro del marco de desarrollos numéricos para sistemas cuánticos de muchos cuerpos, con énfasis en el modelo de Bose-Hubbard. Esto, con el objetivo de entender mejor la imposición de restricciones adicionales para asegurar la validez de los resultados.  Resultados: El número creciente de publicaciones sobre este tema en la última década indica un mayor interés en soluciones para sistemas cuánticos de muchos cuerpos, impulsadas por avances promisorios en materiales superconductores, computación cuántica y otras áreas de impacto.  Conclusiones: Este trabajo exploró los trabajos fundamentales para ayudar a los principiantes a comprender una técnica bien establecida que promete sobrepasar las limitaciones de la computación clásica. El uso de los estados de producto de matrices en los algoritmos DMRG está ganando una tracción significativa en numerosos campos, incluyendo la computación cuántica, el aprendizaje automático y la mecánica estadística, con el fin de abordar los desafíos asociados con los sistemas cuánticos de muchos cuerpos.  Acknowledgments: Este trabajo fue apoyado por la Universidad del Valle bajo el proyecto interno Cl. 71344.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[matrix product states]]></kwd>
<kwd lng="en"><![CDATA[density matrix renormalization group]]></kwd>
<kwd lng="en"><![CDATA[strongly correlated systems]]></kwd>
<kwd lng="en"><![CDATA[Bose-Hubbard model]]></kwd>
<kwd lng="en"><![CDATA[tensor networks]]></kwd>
<kwd lng="es"><![CDATA[estados producto de matrices]]></kwd>
<kwd lng="es"><![CDATA[grupo de renormalización de matriz de densidad]]></kwd>
<kwd lng="es"><![CDATA[sistemas fuertemente correlacionados]]></kwd>
<kwd lng="es"><![CDATA[modelo de Bose-Hubbard]]></kwd>
<kwd lng="es"><![CDATA[redes de tensor]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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