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 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 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 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 Quantum Classical Correspondence and Entanglement in Periodically Driven Spin Systems written by Meenu Kumari and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation sets out to examine some fundamental open questions in quantum physics regarding quantum-classical correspondence in regular versus chaotic systems. Specifically, we study these questions using approaches in quantum information science in an experimentally realized textbook model of quantum chaos - the quantum kicked top (QKT). The effect of classical chaos on the generation of entanglement in spin systems has been a field of active research for a couple of decades. Whether high entanglement in these systems is a hallmark of chaos or not remains a widely debated topic. We explain the connection between entanglement and chaos in spin systems and resolve previous conflicting results. The previous studies have mostly drawn conclusions from numerical work on a few initial states in regular versus chaotic regions. We instead focus on stable and unstable periodic orbits because chaos emerges around unstable periodic orbits. We first propose a new set of criteria for determining whether quantum evolution will correspond to the classical trajectory in a localized manner at stable periodic orbits in periodically driven systems. These criteria can be used to calculate the quantum numbers that will lead to quantum-classical correspondence even in a deep quantum regime, and thus to quantify the well-known Bohr correspondence principle. Next, we analytically show a direct connection between entanglement generation and a measure of delocalization of a quantum state in spin systems. More concretely, we describe a method to calculate an upper bound on entanglement generation in any bipartition of spin systems, where the upper bound is a function of trace distance between the evolved state and the most localized classical-like separable states. This method along with our criteria for localized evolution enables us to explain the behaviour of entanglement in both deep quantum and semiclassical regimes for regular as well as chaotic regions. Hence, our analysis resolves the long-standing debates regarding the connection between classical chaos and quantum entanglement in deep quantum and semiclassical regimes. In addition to the study of entanglement, we perform the first study of nonlocality, and the effect of chaos on its generation in the QKT. Since nonlocality and entanglement are inequivalent quantum resources, the effect of chaos on nonlocality merits an explicit study. Violations of Bell inequalities in the presence of spacelike separation among the subsystems imply nonlocality - meaning nonlocal correlations between subsystems of the total spin system. We show that the QKT evolution can lead to states that violate multiqubit Bell inequalities and hence provides a deterministic method to prepare nonlocal quantum states. Our numerical results suggest a correlation between delocalized evolution of a pure quantum state and generation of nonlocality in the quantum state. We further demonstrate that dynamical tunnelling - a classically forbidden phenomenon - in the QKT leads to the generation of Greenberger-Horne-Zeilinger (GHZ)-like states for even numbers of qubits. We analytically prove that these states are maximally nonlocal. On the other hand, we numerically show that any reduced state of the QKT obtained by tracing out a subsystem of the total spin system does not violate Bell inequalities. We provide an analytical explanation of the numerical results for $2-$qubit reduced states by formulating and proving two general theorems regarding $2-$qubit Bell inequalities. These theorems imply that any $2-$qubit mixed state having a symmetric extension or symmetric purification cannot violate the Clauser-Horne-Shimony-Holt inequality. This highlights fundamental connections between two important and distinct concepts in quantum information science - Bell inequalities and symmetric extension of quantum states. Apart from providing deeper insights into the fundamental questions of quantum-classical correspondence and new approaches to analyze quantum chaos, the methods developed in this thesis can be used to design quantum systems that can efficiently generate entanglement and nonlocality. Thus, our results could have interesting applications in quantum computing and quantum information science.
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 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 Characterizing Entanglement and Quantum Correlations Constrained by Symmetry written by Jordi Tura i Brugués and published by Springer. This book was released on 2016-12-01 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis focuses on the study and characterization of entanglement and nonlocal correlations constrained under symmetries. It includes original results as well as detailed methods and explanations for a number of different threads of research: positive partial transpose (PPT) entanglement in the symmetric states; a novel, experimentally friendly method to detect nonlocal correlations in many-body systems; the non-equivalence between entanglement and nonlocality; and elemental monogamies of correlations. Entanglement and nonlocal correlations constitute two fundamental resources for quantum information processing, as they allow novel tasks that are otherwise impossible in a classical scenario. However, their elusive characterization is still a central problem in quantum information theory. The main reason why such a fundamental issue remains a formidable challenge lies in the exponential growth in complexity of the Hilbert space as well as the space of multipartite correlations. Physical systems of interest, on the other hand, display symmetries that can be exploited to reduce this complexity, opening the possibility that some of these questions become tractable for such systems.
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 Chaos written by Hans-Jürgen Stöckmann and published by Cambridge University Press. This book was released on 1999-10-13 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses quantum chaos, an important area of nonlinear science.
Download or read book Quantum chaos in spin clusters written by Daniel Thomas Robb and published by . This book was released on 1997 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 Exploring Quantum Phases of the Zig zag Chain written by Jon Spalding and published by . This book was released on 2013 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: The spin liquid quantum mechanical state is at the forefront of condensed matter physics and motivates these introductory studies into quantum magnetism on a one-dimensional spin chain. After reviewing some context and history, the approach (exact diagonalization) and the model (Heisenberg Hamiltonian in one dimension with nearest neighbor (nn), next-nearest neighbor (nnn), and a four-site interaction known as a ring exchange (ring)) are described with simple examples for the reader to study. Methods of observation of quantum spin chains are reviewed, including the structure factor which is an important observable. The entanglement entropy is discussed and demonstrated with hand examples. Then, the structure factor is used to demonstrate a phase transition in a Heisenberg model with only nearest neighbor and next-nearest neighbor interactions. Entanglement entropy is used to investigate and compare rectangular and triangular ladders (nn and nnn with and without ring). Entanglement entropy is used to create a surface plot phase diagram for a nn, nnn, ring model for a wide range of interaction energies. Proposals for future studies are presented in the conclusions, including varied boundary conditions, implementing larger system sizes, and investigating interesting regions of the entropy phase diagram, among other possibilities.
Download or read book Philosophy of Quantum Information and Entanglement written by Alisa Bokulich and published by Cambridge University Press. This book was released on 2010-06-10 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent work in quantum information science has produced a revolution in our understanding of quantum entanglement. Scientists now view entanglement as a physical resource with many important applications. These range from quantum computers, which would be able to compute exponentially faster than classical computers, to quantum cryptographic techniques, which could provide unbreakable codes for the transfer of secret information over public channels. These important advances in the study of quantum entanglement and information touch on deep foundational issues in both physics and philosophy. This interdisciplinary volume brings together fourteen of the world's leading physicists and philosophers of physics to address the most important developments and debates in this exciting area of research. It offers a broad spectrum of approaches to resolving deep foundational challenges - philosophical, mathematical, and physical - raised by quantum information, quantum processing, and entanglement. This book is ideal for historians, philosophers of science and physicists.
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:
