Publication: Weak Hopf algebras, Matrix Product Operators and the classification of quantum phases of matter
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2023-10-17
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Universidad Complutense de Madrid
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Abstract
La comprensión de la estructura de entrelazamiento de los sistemas cuánticos de muchos cuerpos es fuerza motriz de crecientes esfuerzos teóricos en las ultimas décadas. Esto ha conducido, en particular, al estudio de las redes tensoriales, un paradigma revolucionario que surgió de la colaboración entre la teoría de la información cuántica y la teoría de la materia condensada. Estos modelos, fácilmente descritos en términos de tensores locales contraídos a lo largo de una estructura gráfica subyacente, resultan sorprendentemente poderosos para describir sistemas cuánticos de muchos cuerpos en términos de sus grados de libertad de entrelazamiento, dilucidar las propiedades esenciales de las fases de la materia cuántica y caracterizar como las diferentes simetrías son codificadas, mediante el análisis de sus tensores constituyentes...
Understanding the entanglement structure of quantum many-body systems is a driving force behind increasing theoretical efforts in recent decades. This has led, in particular, to the study of tensor networks, a revolutionary paradigm that emerged from the interplay between quantum information theory and condensed matter theory. These models, easily described in terms of local tensors contracted along an underlying graph structure, are surprisingly powerful for describing interacting quantum many-body systems in terms of their entanglement degrees of freedom, elucidating the essential properties of phases of quantu mmatter and characterizing how different symmetries are encoded by the analysis of their constituent tensors...
Understanding the entanglement structure of quantum many-body systems is a driving force behind increasing theoretical efforts in recent decades. This has led, in particular, to the study of tensor networks, a revolutionary paradigm that emerged from the interplay between quantum information theory and condensed matter theory. These models, easily described in terms of local tensors contracted along an underlying graph structure, are surprisingly powerful for describing interacting quantum many-body systems in terms of their entanglement degrees of freedom, elucidating the essential properties of phases of quantu mmatter and characterizing how different symmetries are encoded by the analysis of their constituent tensors...
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Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, leída el 19-01-2023