Density Matrix And Tensor Network Renormalization
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Density Matrix And Tensor Network Renormalization
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Author : Tao Xiang
language : en
Publisher: Cambridge University Press
Release Date : 2023-08-31
Density Matrix And Tensor Network Renormalization written by Tao Xiang and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-31 with Science categories.
Renormalization group theory of tensor network states provides a powerful tool for studying quantum many-body problems and a new paradigm for understanding entangled structures of complex systems. In recent decades the theory has rapidly evolved into a universal framework and language employed by researchers in fields ranging from condensed matter theory to machine learning. This book presents a pedagogical and comprehensive introduction to this field for the first time. After an introductory survey on the major advances in tensor network algorithms and their applications, it introduces step-by-step the tensor network representations of quantum states and the tensor-network renormalization group methods developed over the past three decades. Basic statistical and condensed matter physics models are used to demonstrate how the tensor network renormalization works. An accessible primer for scientists and engineers, this book would also be ideal as a reference text for a graduate course in this area.
Density Matrix And Tensor Network Renormalization
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Author : Tao Xiang
language : en
Publisher: Cambridge University Press
Release Date : 2023-08-31
Density Matrix And Tensor Network Renormalization written by Tao Xiang and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-31 with Science categories.
Renormalization group theory of tensor network states provides a powerful tool for studying quantum many-body problems and a new paradigm for understanding entangled structures of complex systems. In recent decades the theory has rapidly evolved into a universal framework and language employed by researchers in fields ranging from condensed matter theory to machine learning. This book presents a pedagogical and comprehensive introduction to this field for the first time. After an introductory survey on the major advances in tensor network algorithms and their applications, it introduces step-by-step the tensor network representations of quantum states and the tensor-network renormalization group methods developed over the past three decades. Basic statistical and condensed matter physics models are used to demonstrate how the tensor network renormalization works. An accessible primer for scientists and engineers, this book would also be ideal as a reference text for a graduate course in this area.
Tensor Network Contractions
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Author : Shi-Ju Ran
language : en
Publisher: Springer Nature
Release Date : 2020-01-27
Tensor Network Contractions written by Shi-Ju Ran and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-27 with Science categories.
Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum many-body physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are not well discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics.
Introduction To Tensor Network Methods
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Author : Simone Montangero
language : en
Publisher: Springer
Release Date : 2018-11-28
Introduction To Tensor Network Methods written by Simone Montangero and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-28 with Science categories.
This volume of lecture notes briefly introduces the basic concepts needed in any computational physics course: software and hardware, programming skills, linear algebra, and differential calculus. It then presents more advanced numerical methods to tackle the quantum many-body problem: it reviews the numerical renormalization group and then focuses on tensor network methods, from basic concepts to gauge invariant ones. Finally, in the last part, the author presents some applications of tensor network methods to equilibrium and out-of-equilibrium correlated quantum matter. The book can be used for a graduate computational physics course. After successfully completing such a course, a student should be able to write a tensor network program and can begin to explore the physics of many-body quantum systems. The book can also serve as a reference for researchers working or starting out in the field.
Tensor Network Contractions
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Author : Maciej Lewenstein
language : en
Publisher:
Release Date : 2020-10-08
Tensor Network Contractions written by Maciej Lewenstein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-08 with Science categories.
Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum many-body physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are not well discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Quantum Chemistry And Dynamics Of Excited States
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Author : Leticia González
language : en
Publisher: John Wiley & Sons
Release Date : 2021-02-01
Quantum Chemistry And Dynamics Of Excited States written by Leticia González and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-01 with Science categories.
An introduction to the rapidly evolving methodology of electronic excited states For academic researchers, postdocs, graduate and undergraduate students, Quantum Chemistry and Dynamics of Excited States: Methods and Applications reports the most updated and accurate theoretical techniques to treat electronic excited states. From methods to deal with stationary calculations through time-dependent simulations of molecular systems, this book serves as a guide for beginners in the field and knowledge seekers alike. Taking into account the most recent theory developments and representative applications, it also covers the often-overlooked gap between theoretical and computational chemistry. An excellent reference for both researchers and students, Excited States provides essential knowledge on quantum chemistry, an in-depth overview of the latest developments, and theoretical techniques around the properties and nonadiabatic dynamics of chemical systems. Readers will learn: ● Essential theoretical techniques to describe the properties and dynamics of chemical systems ● Electronic Structure methods for stationary calculations ● Methods for electronic excited states from both a quantum chemical and time-dependent point of view ● A breakdown of the most recent developments in the past 30 years For those searching for a better understanding of excited states as they relate to chemistry, biochemistry, industrial chemistry, and beyond, Quantum Chemistry and Dynamics of Excited States provides a solid education in the necessary foundations and important theories of excited states in photochemistry and ultrafast phenomena.
Density Matrix Renormalization Group
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Author : Tim Byrnes
language : en
Publisher: timbyrnes
Release Date : 2003
Density Matrix Renormalization Group written by Tim Byrnes and has been published by timbyrnes this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Density matrices categories.
Modelling Non Markovian Quantum Systems Using Tensor Networks
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Author : Aidan Strathearn
language : en
Publisher: Springer Nature
Release Date : 2020-08-31
Modelling Non Markovian Quantum Systems Using Tensor Networks written by Aidan Strathearn and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-31 with Science categories.
This thesis presents a revolutionary technique for modelling the dynamics of a quantum system that is strongly coupled to its immediate environment. This is a challenging but timely problem. In particular it is relevant for modelling decoherence in devices such as quantum information processors, and how quantum information moves between spatially separated parts of a quantum system. The key feature of this work is a novel way to represent the dynamics of general open quantum systems as tensor networks, a result which has connections with the Feynman operator calculus and process tensor approaches to quantum mechanics. The tensor network methodology developed here has proven to be extremely powerful: For many situations it may be the most efficient way of calculating open quantum dynamics. This work is abounds with new ideas and invention, and is likely to have a very significant impact on future generations of physicists.
Density Matrix Renormalization Group Dmrg Based Approaches In Computational Chemistry
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Author : Haibo Ma
language : en
Publisher: Elsevier
Release Date : 2022-08-21
Density Matrix Renormalization Group Dmrg Based Approaches In Computational Chemistry written by Haibo Ma and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-21 with Science categories.
Density Matrix Renormalization Group (DMRG)-based Approaches in Computational Chemistry outlines important theories and algorithms of DMRG-based approaches and explores their use in computational chemistry. Beginning with an introduction to DMRG and DMRG-based approaches, the book goes on to discuss the key theories and applications of DMRG, from DMRG for semi-empirical and ab-initio quantum chemistry, to DMRG in embedded environments, frequency spaces and quantum dynamics. Drawing on the experience of its expert authors, sections detail recent ideas and key developments, providing an up-to-date view of current developments in the field for students and researchers in quantum chemistry. Provides an expertly-curated, consolidated overview of research in the field Includes exercises that support learning and link theory to practice Outlines key theories and algorithms for computational chemistry applications
Tensor Network States And Effective Particles For Low Dimensional Quantum Spin Systems
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Author : Laurens Vanderstraeten
language : en
Publisher: Springer
Release Date : 2017-08-10
Tensor Network States And Effective Particles For Low Dimensional Quantum Spin Systems written by Laurens Vanderstraeten and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-10 with Science categories.
This thesis develops new techniques for simulating the low-energy behaviour of quantum spin systems in one and two dimensions. Combining these developments, it subsequently uses the formalism of tensor network states to derive an effective particle description for one- and two-dimensional spin systems that exhibit strong quantum correlations. These techniques arise from the combination of two themes in many-particle physics: (i) the concept of quasiparticles as the effective low-energy degrees of freedom in a condensed-matter system, and (ii) entanglement as the characteristic feature for describing quantum phases of matter. Whereas the former gave rise to the use of effective field theories for understanding many-particle systems, the latter led to the development of tensor network states as a description of the entanglement distribution in quantum low-energy states.