Tensor Network States And Effective Particles For Low Dimensional Quantum Spin Systems

Author : Laurens Vanderstraeten
Publisher : Springer
Page : 219 pages
File Size : 43,5 Mb
Release : 2017-08-10
Category : Science
ISBN : 9783319641911

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Tensor Network States and Effective Particles for Low-Dimensional Quantum Spin Systems by Laurens Vanderstraeten Pdf

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.

Author : Simone Montangero
Publisher : Springer
Page : 172 pages
File Size : 52,9 Mb
Release : 2018-11-28
Category : Science
ISBN : 9783030014094

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Introduction to Tensor Network Methods by Simone Montangero Pdf

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.

Author : Shi-Ju Ran,Emanuele Tirrito,Cheng Peng,Xi Chen,Luca Tagliacozzo,Gang Su,Maciej Lewenstein
Publisher : Springer Nature
Page : 160 pages
File Size : 50,9 Mb
Release : 2020-01-27
Category : Science
ISBN : 9783030344894

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Tensor Network Contractions by Shi-Ju Ran,Emanuele Tirrito,Cheng Peng,Xi Chen,Luca Tagliacozzo,Gang Su,Maciej Lewenstein Pdf

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.

Author : John B. Parkinson,Damian J. J. Farnell
Publisher : Springer Science & Business Media
Page : 159 pages
File Size : 45,7 Mb
Release : 2010-09-20
Category : Science
ISBN : 9783642132896

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An Introduction to Quantum Spin Systems by John B. Parkinson,Damian J. J. Farnell Pdf

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.

Author : Aidan Strathearn
Publisher : Springer Nature
Page : 113 pages
File Size : 47,8 Mb
Release : 2020-08-31
Category : Science
ISBN : 9783030549756

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Modelling Non-Markovian Quantum Systems Using Tensor Networks by Aidan Strathearn Pdf

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.

Author : Stefanie Czischek
Publisher : Springer Nature
Page : 205 pages
File Size : 50,7 Mb
Release : 2020-08-27
Category : Science
ISBN : 9783030527150

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Neural-Network Simulation of Strongly Correlated Quantum Systems by Stefanie Czischek Pdf

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.

Author : Tao Xiang
Publisher : Cambridge University Press
Page : 456 pages
File Size : 55,7 Mb
Release : 2023-08-31
Category : Science
ISBN : 9781009398718

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Density Matrix and Tensor Network Renormalization by Tao Xiang Pdf

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.

Author : H. T. Diep
Publisher : World Scientific
Page : 644 pages
File Size : 43,5 Mb
Release : 2013
Category : Science
ISBN : 9789814440745

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Frustrated Spin Systems by H. T. Diep Pdf

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."

Author : Konstantin Efetov
Publisher : Cambridge University Press
Page : 470 pages
File Size : 47,8 Mb
Release : 1999-09-13
Category : Mathematics
ISBN : 0521663822

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Supersymmetry in Disorder and Chaos by Konstantin Efetov Pdf

This book provides a comprehensive treatment of the ideas and applications of supersymmetry.

Author : Mukund Rangamani,Tadashi Takayanagi
Publisher : Springer
Page : 246 pages
File Size : 54,7 Mb
Release : 2017-05-08
Category : Science
ISBN : 9783319525730

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Holographic Entanglement Entropy by Mukund Rangamani,Tadashi Takayanagi Pdf

This book provides a comprehensive overview of developments in the field of holographic entanglement entropy. Within the context of the AdS/CFT correspondence, it is shown how quantum entanglement is computed by the area of certain extremal surfaces. The general lessons one can learn from this connection are drawn out for quantum field theories, many-body physics, and quantum gravity. An overview of the necessary background material is provided together with a flavor of the exciting open questions that are currently being discussed. The book is divided into four main parts. In the first part, the concept of entanglement, and methods for computing it, in quantum field theories is reviewed. In the second part, an overview of the AdS/CFT correspondence is given and the holographic entanglement entropy prescription is explained. In the third part, the time-dependence of entanglement entropy in out-of-equilibrium systems, and applications to many body physics are explored using holographic methods. The last part focuses on the connection between entanglement and geometry. Known constraints on the holographic map, as well as, elaboration of entanglement being a fundamental building block of geometry are explained. The book is a useful resource for researchers and graduate students interested in string theory and holography, condensed matter and quantum information, as it tries to connect these different subjects linked by the common theme of quantum entanglement.

Author : Sevag Gharibian,Yichen Huang,Zeph Landau,Seung Woo Shin
Publisher : Unknown
Page : 140 pages
File Size : 43,9 Mb
Release : 2015-09-30
Category : Computers
ISBN : 1680830066

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Quantum Hamiltonian Complexity by Sevag Gharibian,Yichen Huang,Zeph Landau,Seung Woo Shin Pdf

This monograph provides an introduction to the rapidly growing field of Quantum Hamiltonian Complexity, which includes the study of quantum constraint satisfaction problems. It provides a computer science-oriented introduction to the subject in order to help bridge the language barrier between computer scientists and physicists in the field.

Author : Philip W. Anderson
Publisher : World Scientific
Page : 206 pages
File Size : 54,6 Mb
Release : 1997
Category : Science
ISBN : 9810232314

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Concepts in Solids by Philip W. Anderson Pdf

These lecture notes constitute a course on a number of central concepts of solid state physics ? classification of solids, band theory, the developments in one-electron band theory in the presence of perturbation, effective Hamiltonian theory, elementary excitations and the various types of collective elementary excitation (excitons, spin waves and phonons), the Fermi liquid, ferromagnetic spin waves, antiferromagnetic spin waves and the theory of broken symmetry.The book can be used in conjunction with a survey course in solid state physics, or as the basis of a first graduate-level course. It can be read by anyone who has had basic grounding in quantum mechanics.

Author : Claudine Lacroix,Philippe Mendels,Frédéric Mila
Publisher : Springer Science & Business Media
Page : 682 pages
File Size : 44,5 Mb
Release : 2011-01-12
Category : Science
ISBN : 9783642105890

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Introduction to Frustrated Magnetism by Claudine Lacroix,Philippe Mendels,Frédéric Mila Pdf

The field of highly frustrated magnetism has developed considerably and expanded over the last 15 years. Issuing from canonical geometric frustration of interactions, it now extends over other aspects with many degrees of freedom such as magneto-elastic couplings, orbital degrees of freedom, dilution effects, and electron doping. Its is thus shown here that the concept of frustration impacts on many other fields in physics than magnetism. This book represents a state-of-the-art review aimed at a broad audience with tutorial chapters and more topical ones, encompassing solid-state chemistry, experimental and theoretical physics.

Author : Eva Pavarini,Erik Koch,Ulrich Schollwöck
Publisher : Forschungszentrum Jülich
Page : 562 pages
File Size : 49,6 Mb
Release : 2013
Category : Electronic
ISBN : 9783893368846

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Emergent Phenomena in Correlated Matter by Eva Pavarini,Erik Koch,Ulrich Schollwöck Pdf

Author : Alexander Krasnitz,Yuri A Kubyshin,Robertus Potting,P Sa
Publisher : World Scientific
Page : 238 pages
File Size : 49,6 Mb
Release : 1999-08-13
Category : Electronic
ISBN : 9789814543576

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Exact Renormalization Group, The - Proceedings Of The Workshop by Alexander Krasnitz,Yuri A Kubyshin,Robertus Potting,P Sa Pdf

The subject of the exact renormalization group started from pioneering work by Wegner and Houghton in the early seventies and, a decade later, by Polchinski, who formulated the Wilson renormalization group for field theory. In the past decade considerable progress has been made in this field, which includes the development of alternative formulations of the approach and of powerful techniques for solving the exact renormalization group equations, as well as widening of the scope of the exact renormalization group method to include fermions and gauge fields. In particular, two very recent results, namely the manifestly gauge-invariant formulation of the exact renormalization group equation and the proof of the c-theorem in four dimensions, are presented in this volume.