Download or read book Entanglement in an Open Heisenberg Spin Chain written by Subhendu Paul and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We analyze the time evolution of a spin chain of three qubits with nearest-neighbour Heisenberg XX interaction, coupled to two thermal reservoirs. We use the 'reduced density matrix approach' to calculate the populations and correlations (concurrence) among the spins. The spin-reservoir interaction is of the energy conserving type. This allows us to analyze the evolution analytically without approximations - yielding explicit, yet complicated formulas for the spin dynamics. To analyze the latter and discuss it as a function of the various physical parameters and time (intial conditions, termperatures, coupling strenghts), we resort to numerical methods. Our main finding is that the external noise (coupling to reservoirs) causes the appearence of an asymptotic, stationary (time-periodic) regime for the dynamics of concurrence. We discuss the dependence of the relaxation time and the characteristics of the regime itself, on the various parameters.

Download or read book Entanglement Dynamics in the Heisenberg Antiferromagnetic Spin Chain Model written by Spencer Ambrose Smith and published by . This book was released on 2004 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Operator Spreading and Entangling in a Quantum Chaotic Spin Chain written by Cheryne Jonay and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "We study operator dynamics and entanglement in a quantum chaotic Heisenberg spin chain. Specifically, we are interested in how these two processes - spreading and entangling - are related. What we find is that they are distinct processes: the dynamics of (i) the spreading of local operators, (ii) the width of the 'front' of this moving operator, (iii) the entanglemwent production, are characterized by different time scales. In a finite size system an initially local operator spreads from one end to the other on one time scale (given by the so-called butterfly speed vB), but becomes an essentially random operator (a fully entangled operator) on the full system on a longer time scale (given by the slower entanglement speed vopEE). The moving front of the operator broadens with time, but sublinearly, perhaps diffusively as ~ the square root of t. For the spreading operator, we relate the local rate of entanglement production dS/dt and the spatial gradient of the entanglement across the bipartite cut as the cut is moved, dS/dx. Following Nahum et al., we propose that dSdt = +-vB dS/dx sets the entanglement profile for the spreading operator. We conclude that the entanglement within the spreading operator is "volume-law", but is less than that of a fully random operator. Only after the operator reaches an end of the system does it become maximally entangled."

Download or read book Entanglement in Spin Chains written by Abolfazl Bayat and published by Springer Nature. This book was released on 2022-09-26 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers recent developments in the understanding, quantification, and exploitation of entanglement in spin chain models from both condensed matter and quantum information perspectives. Spin chain models are at the foundation of condensed matter physics and quantum information technologies and elucidate many fundamental phenomena such as information scrambling, quantum phase transitions, and many-body localization. Moreover, many quantum materials and emerging quantum devices are well described by spin chains. Comprising accessible, self-contained chapters written by leading researchers, this book is essential reading for graduate students and researchers in quantum materials and quantum information. The coverage is comprehensive, from the fundamental entanglement aspects of quantum criticality, non-equilibrium dynamics, classical and quantum simulation of spin chains through to their experimental realizations, and beyond into machine learning applications.

Download or read book Entanglement in Spin Chains written by Abolfazl Bayat and published by Springer. This book was released on 2023-09-28 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers recent developments in the understanding, quantification, and exploitation of entanglement in spin chain models from both condensed matter and quantum information perspectives. Spin chain models are at the foundation of condensed matter physics and quantum information technologies and elucidate many fundamental phenomena such as information scrambling, quantum phase transitions, and many-body localization. Moreover, many quantum materials and emerging quantum devices are well described by spin chains. Comprising accessible, self-contained chapters written by leading researchers, this book is essential reading for graduate students and researchers in quantum materials and quantum information. The coverage is comprehensive, from the fundamental entanglement aspects of quantum criticality, non-equilibrium dynamics, classical and quantum simulation of spin chains through to their experimental realizations, and beyond into machine learning applications.

Download or read book The Theory of Open Quantum Systems written by Heinz-Peter Breuer and published by Oxford University Press, USA. This book was released on 2002 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats the central physical concepts and mathematical techniques used to investigate the dynamics of open quantum systems. To provide a self-contained presentation the text begins with a survey of classical probability theory and with an introduction into the foundations of quantum mechanics with particular emphasis on its statistical interpretation. The fundamentals of density matrix theory, quantum Markov processes and dynamical semigroups are developed. The most important master equations used in quantum optics and in the theory of quantum Brownian motion are applied to the study of many examples. Special attention is paid to the theory of environment induced decoherence, its role in the dynamical description of the measurement process and to the experimental observation of decohering Schrodinger cat states. The book includes the modern formulation of open quantum systems in terms of stochastic processes in Hilbert space. Stochastic wave function methods and Monte Carlo algorithms are designed and applied to important examples from quantum optics and atomic physics, such as Levy statistics in the laser cooling of atoms, and the damped Jaynes-Cummings model. The basic features of the non-Markovian quantum behaviour of open systems are examined on the basis of projection operator techniques. In addition, the book expounds the relativistic theory of quantum measurements and discusses several examples from a unified perspective, e.g. non-local measurements and quantum teleportation. Influence functional and super-operator techniques are employed to study the density matrix theory in quantum electrodynamics and applications to the destruction of quantum coherence are presented. The text addresses graduate students and lecturers in physics and applied mathematics, as well as researchers with interests in fundamental questions in quantum mechanics and its applications. Many analytical methods and computer simulation techniques are developed and illustrated with the help of numerous specific examples. Only a basic understanding of quantum mechanics and of elementary concepts of probability theory is assumed.

Download or read book Quantum Many Body Physics in Open Systems Measurement and Strong Correlations written by Yuto Ashida and published by Springer Nature. This book was released on 2020-01-06 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the fundamental aspects of many-body physics in quantum systems open to an external world. Recent remarkable developments in the observation and manipulation of quantum matter at the single-quantum level point to a new research area of open many-body systems, where interactions with an external observer and the environment play a major role. The first part of the book elucidates the influence of measurement backaction from an external observer, revealing new types of quantum critical phenomena and out-of-equilibrium dynamics beyond the conventional paradigm of closed systems. In turn, the second part develops a powerful theoretical approach to study the in- and out-of-equilibrium physics of an open quantum system strongly correlated with an external environment, where the entanglement between the system and the environment plays an essential role. The results obtained here offer essential theoretical results for understanding the many-body physics of quantum systems open to an external world, and can be applied to experimental systems in atomic, molecular and optical physics, quantum information science and condensed matter physics.

Download or read book Strongly Correlated Systems Coherence And Entanglement written by J M P Carmelo and published by World Scientific. This book was released on 2007-07-12 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a collection of review papers on recent work in the connected areas of strongly correlated systems, the effects of coherence on macroscopic systems, and entanglement in quantum systems. These areas have attracted considerable interest due to their complexity and associated unexpected nontrivial phenomena, and also due to their potential applications in various fields, from materials science to information technology. The coverage includes strongly correlated electronic systems such as low-dimensional complex materials, ordered and disordered spin systems, and aspects of the physics of manganites and graphene, both in equilibrium and far from equilibrium.

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.

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.

Download or read book Topological Aspects of Condensed Matter Physics written by Claudio Chamon and published by Oxford University Press. This book was released on 2017-02-16 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains lecture notes by world experts on one of the most rapidly growing fields of research in physics. Topological quantum phenomena are being uncovered at unprecedented rates in novel material systems. The consequences are far reaching, from the possibility of carrying currents and performing computations without dissipation of energy, to the possibility of realizing platforms for topological quantum computation.The pedagogical lectures contained in this book are an excellent introduction to this blooming field. The lecture notes are intended for graduate students or advanced undergraduate students in physics and mathematics who want to immerse in this exciting XXI century physics topic. This Les Houches Summer School presents an overview of this field, along with a sense of its origins and its placement on the map of fundamental physics advancements. The School comprised a set of basic lectures (part 1) aimed at a pedagogical introduction of the fundamental concepts, which was accompanied by more advanced lectures (part 2) covering individual topics at the forefront of today's research in condensed-matter physics.

Download or read book Entanglement in Spin chains written by Shai Gad Machnes and published by . This book was released on 2005 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Entanglement Metrics for Quantum Spin Chains written by Krishan Canzius and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Quantum Theory Concepts and Methods written by A. Peres and published by Springer Science & Business Media. This book was released on 2006-06-01 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are many excellent books on quantum theory from which one can learn to compute energy levels, transition rates, cross sections, etc. The theoretical rules given in these books are routinely used by physicists to compute observable quantities. Their predictions can then be compared with experimental data. There is no fundamental disagreement among physicists on how to use the theory for these practical purposes. However, there are profound differences in their opinions on the ontological meaning of quantum theory. The purpose of this book is to clarify the conceptual meaning of quantum theory, and to explain some of the mathematical methods which it utilizes. This text is not concerned with specialized topics such as atomic structure, or strong or weak interactions, but with the very foundations of the theory. This is not, however, a book on the philosophy of science. The approach is pragmatic and strictly instrumentalist. This attitude will undoubtedly antagonize some readers, but it has its own logic: quantum phenomena do not occur in a Hilbert space, they occur in a laboratory.

Download or read book Momentum space Entanglement in Quantum Spin Chains written by Rex Oliver Lundgren and published by . This book was released on 2016 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, the momentum-space entanglement properties of several quantum spin chains are investigated. In the second chapter we re- view important results on many-body entanglement. In the third chapter, we numerically study the momentum-space entanglement spectra of bosonic and fermionic formulations of the spin-1/2 XXZ chain [Phys. Rev. Lett. 113, 256404 (2014)]. We investigate the behavior of the entanglement gaps, present in both formulations, across quantum phase transitions in the XXZ chain. In both cases, finite size scaling suggests that the entanglement gap closure does not occur at the physical transition points. For bosons, we find that the entan- glement gap depends on the scaling dimension of the conformal field theory as varied by the X X Z anisotropy. For fermions, the infinite entanglement gap present at the XX point persists well past the phase transition at the Heisenberg point. We elaborate on how this may support the numerical study of phase transitions. In the third chapter, we advocate that in certain critical spin chains a gap in the momentum-space entanglement spectrum separates the universal part of the spectrum, which is determined by the associated conformal field theory, from the non-universal part, which is specific to the model [arXiv:1512.09030]. We provide affirmative evidence from multicritical spin-1 chains with low energy sectors described by the SU(2)2 or the SU(3)1 Wess-Zumino-Witten model. In chapter four, we study momentum- space en- tanglement in quantum spin-half ladders [Phys. Rev. B 93, 125107 (2016)]. When the system is gapped, we analytically find the momentum-space entan- glement Hamiltonian is described by a chiral conformal field theory with a central charge of two. When the system is gapless, the entanglement Hamil- tonian consists of one gapless mode that is linear in subsystem momentum and one mode with a flat dispersion relation. We also analytically include the effect of a certain irrelevant terms (in the renormalization group sense) on the entanglement spectrum. In chapter six, we investigate the momentum- space entanglement spectrum after a quantum quench [arXiv:1603.01997]. We show that the momentum-space entanglement spectrum of the XXZ spin- half chain possesses many universal features both in equilibrium and after a quantum quench.

Download or read book Integrability of a Deformed Heisenberg Spin chain written by Denis Erkal and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Quantum Inverse Scattering Method and Correlation Functions written by V. E. Korepin and published by Cambridge University Press. This book was released on 1997-03-06 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quantum inverse scattering method is a means of finding exact solutions of two-dimensional models in quantum field theory and statistical physics (such as the sine-Go rdon equation or the quantum non-linear Schrödinger equation). These models are the subject of much attention amongst physicists and mathematicians.The present work is an introduction to this important and exciting area. It consists of four parts. The first deals with the Bethe ansatz and calculation of physical quantities. The authors then tackle the theory of the quantum inverse scattering method before applying it in the second half of the book to the calculation of correlation functions. This is one of the most important applications of the method and the authors have made significant contributions to the area. Here they describe some of the most recent and general approaches and include some new results.The book will be essential reading for all mathematical physicists working in field theory and statistical physics.