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 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 Quantum Entanglement in Random Antiferromagnetic Spin Chains written by Thomas S. Jackson and published by . This book was released on 2003 with total page 0 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 Entanglement in Spain Chains written by Abolfazl Bayat and published by . This book was released on 2022 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 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 The Bethe Wavefunction written by Michel Gaudin and published by Cambridge University Press. This book was released on 2014-03-06 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Michel Gaudin's book La fonction d'onde de Bethe is a uniquely influential masterpiece on exactly solvable models of quantum mechanics and statistical physics. Available in English for the first time, this translation brings his classic work to a new generation of graduate students and researchers in physics. It presents a mixture of mathematics interspersed with powerful physical intuition, retaining the author's unmistakably honest tone. The book begins with the Heisenberg spin chain, starting from the coordinate Bethe Ansatz and culminating in a discussion of its thermodynamic properties. Delta-interacting bosons (the Lieb-Liniger model) are then explored, and extended to exactly solvable models associated to a reflection group. After discussing the continuum limit of spin chains, the book covers six- and eight-vertex models in extensive detail, from their lattice definition to their thermodynamics. Later chapters examine advanced topics such as multi-component delta-interacting systems, Gaudin magnets and the Toda chain.

Download or read book Entanglement Between Noncomplementary Parts of Many Body Systems written by Hannu Christian Wichterich and published by Springer Science & Business Media. This book was released on 2011-05-18 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis investigates the structure and behaviour of entanglement, the purely quantum mechanical part of correlations, in many-body systems, employing both numerical and analytical techniques at the interface of condensed matter theory and quantum information theory. Entanglement can be seen as a precious resource which, for example, enables the noiseless and instant transmission of quantum information, provided the communicating parties share a sufficient "amount" of it. Furthermore, measures of entanglement of a quantum mechanical state are perceived as useful probes of collective properties of many-body systems. For instance, certain measures are capable of detecting and classifying ground-state phases and, particularly, transition (or critical) points separating such phases. Chapters 2 and 3 focus on entanglement in many-body systems and its use as a potential resource for communication protocols. They address the questions of how a substantial amount of entanglement can be established between distant subsystems, and how efficiently this entanglement could be "harvested" by way of measurements. The subsequent chapters 4 and 5 are devoted to universality of entanglement between large collections of particles undergoing a quantum phase transition, where, despite the enormous complexity of these systems, collective properties including entanglement no longer depend crucially on the microscopic details.

Download or read book Quantum Chaos and Entanglement in Spin chains written by Thomas Orlando Boness and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Engineered Dissipation Induced Entanglement Transition in Quantum Spin Chains from Logarithmic Growth to Area Law written by Thomas Botzung and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Quantum Chaos and Entanglement in Spin chains written by T. O. Boness and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Entanglement Perturbation Theory for Antiferromagnetic Spin Chains written by Lihua Wang and published by . This book was released on 2009 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we use the recently developed Entanglement Perturbation Theory (EPT) to solve antiferromagnetic spin chain problems, for both spin [half] and spin 1. We firs use EPT-g (EPT algorithm for ground state) to get the ground state properties. We calculated precisely energies, magnetization and spin-spin correlations. The precision of the long range spin-spin correlation functions for spin [half] chains is unprecedented. Due to its special structure, we also use EPT-g to calculate the first[sic] excited state properties for spin 1 chains. Hence we plotted the phase diagram for spin 1 xxz chains. Also a generalization of EPT (EPT-e) for elementary excitation in one dimension determined the spin-triplet magnon spectrum for spin 1 chain for the firs time for the entire Brillouin zone, including the Haldane gap at k = [pi].The spin chains, the 2D&3D Ising models, the 1D &2D Hubbard models and the Bose-Hubbard model whose study by EPT is recently started represent a variety of strongly correlated many body systems with translational symmetry. Namely EPT is a general method for them. On the other hand, the successful application of EPT-e indicated EPT's potential to study the inhomogeneous quantum systems.

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 Maximal Entanglement written by Alba Cervera Lierta and published by . This book was released on 2019 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The aim of this thesis is to study the quantum entanglement and, in particular, under which circumstances is maximum.In the first place, Bell's inequalities are analyzed from an operational point of view. In particular, we focus on those involving qutrits. The states that maximally violate these inequalities are of the GHZ type, for inequalities involving qubits, and little deformations of GHZ state, for those involving qutrits. This result shows that, although maximum entanglement and non-locality are very close concepts, they are not equivalent.In the second place, multipartite entanglement in spin chains is studied. We use as a figure of merit the hyperdeterminant and two polynomial invariants, S and T. These figures quantify a specific type of quadripartite entanglement, as demonstrated by an analysis of well-known quantum states such as the GHZ or W. In an Ising spin chain, we observe a pronounced peak near the quantum phase transition. Similar results are observed for the XXZ and Haldane- Shastry models for the case of the S and T invariants. For that reason, we conclude that these figures of merit are sensitive to quantum phase transitions.The second part of the thesis focuses on the field of quantum computing. This field has experienced a significant expansion in recent years. Due to this growth, several companies have started to develop prototypes of quantum computers. For this reason, one line of research in quantum computing is to propose methods to benchmark these machines.One of the methods presented in this thesis consists of the exact simulation of a XY spin chain. We propose a circuit that diagonalizes the XY Hamiltonian, which allows simulating time evolution and thermal states as well. Since this model is exactly solvable, the results obtained from a quantum computer can be compared with the theoretical solution. After running this circuit for four qubits on two IBM computers and one from Rigetti computing company, we obtain worse results than expected. With this, we conclude that there are error sources that, in general, are not being taken into account and that become relevant even in such small circuits.Moreover, we propose another method to test quantum computers performance: the simulation of absolutely maximally entangled states. The implementation of these circuits is a hard but necessary test for a quantum computer since the advantage of quantum algorithms lies in the generation of entanglement.Finally, we study the generation of entanglement at the most fundamental level: particle physics. We obtain that the QED interaction at tree-level is dictated by the imposition of maximal entanglement in outgoing particles. We apply the same philosophy in processes involving weak neutral currents obtaining that the weak mixing angle must be pi / 6, very close to the experimental value." -- TDX.

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.