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Tensor Network States And Effective Particles For Low Dimensional Quantum Spin Systems
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Book Synopsis Tensor Network States and Effective Particles for Low-Dimensional Quantum Spin Systems by : Laurens Vanderstraeten
Download or read book Tensor Network States and Effective Particles for Low-Dimensional Quantum Spin Systems written by Laurens Vanderstraeten and published by Springer. This book was released on 2017-08-10 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Tensor Network States Intwo Dimensional Quantum Spin Systems by : 蕭信智
Download or read book Tensor Network States Intwo Dimensional Quantum Spin Systems written by 蕭信智 and published by . This book was released on 2010 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Tensor Network Contractions by : Shi-Ju Ran
Download or read book Tensor Network Contractions written by Shi-Ju Ran and published by Springer Nature. This book was released on 2020-01-27 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Tensor Network Methods by : Simone Montangero
Download or read book Introduction to Tensor Network Methods written by Simone Montangero and published by Springer. This book was released on 2018-11-28 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Tensor Network Methods for Low-dimensional Quantum Systems by : Jheng-Wei Li
Download or read book Tensor Network Methods for Low-dimensional Quantum Systems written by Jheng-Wei Li and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Topological Phenomena in Tensor Network States of Quantum Spin Systems by : Mohsin Iqbal
Download or read book Topological Phenomena in Tensor Network States of Quantum Spin Systems written by Mohsin Iqbal and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to Quantum Spin Systems by : John B. Parkinson
Download or read book An Introduction to Quantum Spin Systems written by John B. Parkinson and published by Springer Science & Business Media. This book was released on 2010-09-20 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topic of lattice quantum spin systems is a fascinating and by now well established branch of theoretical physics. Based on a set of lectures, this book has a level of detail missing from others, and guides the reader through the fundamentals of the field.
Book Synopsis Modelling Non-Markovian Quantum Systems Using Tensor Networks by : Aidan Strathearn
Download or read book Modelling Non-Markovian Quantum Systems Using Tensor Networks written by Aidan Strathearn and published by Springer Nature. This book was released on 2020-08-31 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Neural-Network Simulation of Strongly Correlated Quantum Systems by : Stefanie Czischek
Download or read book Neural-Network Simulation of Strongly Correlated Quantum Systems written by Stefanie Czischek and published by Springer Nature. This book was released on 2020-08-27 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum systems with many degrees of freedom are inherently difficult to describe and simulate quantitatively. The space of possible states is, in general, exponentially large in the number of degrees of freedom such as the number of particles it contains. Standard digital high-performance computing is generally too weak to capture all the necessary details, such that alternative quantum simulation devices have been proposed as a solution. Artificial neural networks, with their high non-local connectivity between the neuron degrees of freedom, may soon gain importance in simulating static and dynamical behavior of quantum systems. Particularly promising candidates are neuromorphic realizations based on analog electronic circuits which are being developed to capture, e.g., the functioning of biologically relevant networks. In turn, such neuromorphic systems may be used to measure and control real quantum many-body systems online. This thesis lays an important foundation for the realization of quantum simulations by means of neuromorphic hardware, for using quantum physics as an input to classical neural nets and, in turn, for using network results to be fed back to quantum systems. The necessary foundations on both sides, quantum physics and artificial neural networks, are described, providing a valuable reference for researchers from these different communities who need to understand the foundations of both.
Book Synopsis Tensor Network Algorithms for Three-dimensional Quantum Systems by : Patrick Vlaar
Download or read book Tensor Network Algorithms for Three-dimensional Quantum Systems written by Patrick Vlaar and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Strongly correlated systems can give rise to many types of fascinating emergent behavior, such as superconductivity or exotic magnetic phases. Numerical approaches have become essential tools to further our understanding of these systems. An important family is formed by algorithms based on tensor networks. In recent decades, these methods have turned into vital tools to study one- and two-dimensional quantum systems. Extensions of these algorithms to three-dimensional systems, though, have been relatively unexplored. The goal of this thesis is to develop new algorithms to study three-dimensional quantum systems. We make use of a tensor network Ansatz called the infinite projected entangled-pair state (iPEPS), which allows us to directly probe the thermodynamic limit. The main technical challenge is to find ways to evaluate expectation values, which require a contraction of the tensor network. In this thesis, we develop several efficient contraction algorithms both for general three-dimensional quantum systems and for layered two-dimensional quantum systems with weak interlayer coupling. We apply these algorithms to study the Shastry-Sutherland model, which closely describes the layered compound SrCu2(BO3)2. A discrepancy exists, however, in the extent of the plaquette phase, which is significantly smaller in the compound compared to the model. Through our simulations, we find that a possible explanation could be the interlayer coupling, which strongly reduces the extent of the plaquette phase already at weak coupling. With this thesis, we hope to show the potential of tensor networks for the accurate study of three-dimensional strongly-correlated quantum systems."--
Book Synopsis Density Matrix and Tensor Network Renormalization by : Tao Xiang
Download or read book Density Matrix and Tensor Network Renormalization written by Tao Xiang and published by Cambridge University Press. This book was released on 2023-08-31 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Tensor Network Descriptions of Quantum Entanglement in Path Integrals, Thermalisation and Machine Learning by : Andrew Hallam
Download or read book Tensor Network Descriptions of Quantum Entanglement in Path Integrals, Thermalisation and Machine Learning written by Andrew Hallam and published by . This book was released on 2019 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the major ways in which quantum mechanics differs from classical mechanics is the existence of special quantum correlations - entanglement. Typical quantum states are highly entangled, making them complex and inefficient to represent. Physically interesting states are unusual, they are only weakly entangled. By restricting ourselves to weak entanglement, efficient representations of quantum states can be found. A tensor network is constructed by taking objects called tensors that encode spatially local information and gluing them together to create a large network that describes a complex quantum state. The manner in which the tensors are connected defines the entanglement structure of the quantum state. Tensors networks are therefore a natural framework for describing physical behaviour of complex quantum systems. In this thesis we utilize tensor networks to solve a number of interesting problems. Firstly, we study a Feynman path integral written over tensor network states. As a sum over classical trajectories, a Feynman path integral can struggle to capture entanglement. Combining the path integral with tensor networks overcomes this.We consider the effect of quadratic fluctuations on the tensor network path integral and calculate corrections to observables numerically and analytically. We also study the time evolution of complex quantum systems. By projecting quantum dynamics onto a classical phase space defined using tensor networks, we relate thermal behaviour of quantum systems to classical chaos. In doing so we demonstrate a relationship between entanglement growth and chaos. By studying the dynamics of coupled quantum chains we also gain insight into how quantum correlations spread over time. As noted, tensor networks are remarkably efficient. In the final section of this thesis we use tensor networks to create compressed machine learning algorithms. Their efficiency means that tensor networks can use $50$ times fewer parameters with no significant decrease in performance.
Book Synopsis Frustrated Spin Systems by : H. T. Diep
Download or read book Frustrated Spin Systems written by H. T. Diep and published by World Scientific. This book was released on 2013 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers all principal aspects of currently investigated frustrated systems, from exactly solved frustrated models to real experimental frustrated systems, going through renormalization group treatment, Monte Carlo investigation of frustrated classical Ising and vector spin models, low-dimensional systems, spin ice and quantum spin glass. The reader can OCo within a single book OCo obtain a global view of the current research development in the field of frustrated systems.This new edition is updated with recent theoretical, numerical and experimental developments in the field of frustrated spin systems. The first edition of the book appeared in 2005. In this edition, more recent works until 2012 are reviewed. It contains nine chapters written by researchers who have actively contributed to the field. Many results are from recent works of the authors.The book is intended for postgraduate students as well as researchers in statistical physics, magnetism, materials science and various domains where real systems can be described with the spin language. Explicit demonstrations of formulas and full arguments leading to important results are given where it is possible to do so."
Book Synopsis Tensor Network States by : Justin Reyes
Download or read book Tensor Network States written by Justin Reyes and published by . This book was released on 2020 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensor network states are ubiquitous in the investigation of quantum many-body (QMB) physics. Their advantage over other state representations is evident from their reduction in the computational complexity required to obtain various quantities of interest, namely observables. Additionally, they provide a natural platform for investigating entanglement properties within a system. In this dissertation, we develop various novel algorithms and optimizations to tensor networks for the investigation of QMB systems, including classical and quantum circuits. Specifically, we study optimizations for the two-dimensional Ising model in a transverse field, we create an algorithm for the k-SAT problem, and we study the entanglement properties of random unitary circuits. In addition to these applications, we reinterpret renormalization group principles from QMB physics in the context of machine learning to develop a novel algorithm for the tasks of classification and regression, and then utilize machine learning architectures for the time evolution of operators in QMB systems.
Book Synopsis Tensor Network Contractions by : Maciej Lewenstein
Download or read book Tensor Network Contractions written by Maciej Lewenstein and published by . This book was released on 2020-10-08 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Exact Tensor Network Ansatz for Strongly Interacting Systems by : Michael P. Zaletel
Download or read book Exact Tensor Network Ansatz for Strongly Interacting Systems written by Michael P. Zaletel and published by . This book was released on 2014 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: It appears that the tensor network ansatz, while not quite complete, is an efficient coordinate system for the tiny subset of a many-body Hilbert space which can be realized as a low energy state of a local Hamiltonian. However, we don't fully understand precisely which phases are captured by the tensor network ansatz, how to compute their physical observables (even numerically), or how to compute a tensor network representation for a ground state given a microscopic Hamiltonian. These questions are algorithmic in nature, but their resolution is intimately related to understanding the nature of quantum entanglement in many-body systems. For this reason it is useful to compute the tensor network representation of various `model' wavefunctions representative of different phases of matter; this allows us to understand how the entanglement properties of each phase are expressed in the tensor network ansatz, and can serve as test cases for algorithm development. Condensed matter physics has many illuminating model wavefunctions, such as Laughlin's celebrated wave function for the fractional quantum Hall effect, the Bardeen-Cooper-Schrieffer wave function for superconductivity, and Anderson's resonating valence bond ansatz for spin liquids. This thesis presents some results on exact tensor network representations of these model wavefunctions. In addition, a tensor network representation is given for the time evolution operator of a long-range one-dimensional Hamiltonian, which allows one to numerically simulate the time evolution of power-law interacting spin chains as well as two-dimensional strips and cylinders.
Book Synopsis Emergent Phenomena in Correlated Matter by : Eva Pavarini
Download or read book Emergent Phenomena in Correlated Matter written by Eva Pavarini and published by Forschungszentrum Jülich. This book was released on 2013 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt:
