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Tensor Network States and Effective Particles for Low-Dimensional Quantum Spin Systems

2017-08-10 Science
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Release : 2017-08-10
Genre : Science
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Book Rating : 913/5 ( reviews)

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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. This book was released on 2017-08-10. 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.

Tensor Network States Intwo Dimensional Quantum Spin Systems

2010
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Release : 2010
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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. This book was released on 2010. Available in PDF, EPUB and Kindle. Book excerpt:

Tensor Network Contractions

2020-01-27 Science
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Release : 2020-01-27
Genre : Science
Kind : eBook
Book Rating : 894/5 ( reviews)

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Book Synopsis Tensor Network Contractions by : Shi-Ju Ran

Download or read book Tensor Network Contractions written by Shi-Ju Ran. This book was released on 2020-01-27. 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.

Introduction to Tensor Network Methods

2018-11-28 Science
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Release : 2018-11-28
Genre : Science
Kind : eBook
Book Rating : 096/5 ( reviews)

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Book Synopsis Introduction to Tensor Network Methods by : Simone Montangero

Download or read book Introduction to Tensor Network Methods written by Simone Montangero. This book was released on 2018-11-28. 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.

Tensor Network Methods for Low-dimensional Quantum Systems

2022
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Release : 2022
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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. This book was released on 2022. Available in PDF, EPUB and Kindle. Book excerpt:

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