Download or read book Disorder Operators Entanglement Entropies and Dynamic Spectra in Strongly Correlated Quantum Spin Systems written by 赵家瑞 and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Novel Transport in Quantum Phases and Entanglement Dynamics Beyond Equilibrium written by Joseph C. Szabo and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding and identifying quantum phases have been longstanding pursuits in the field condensed matter physics. The most exciting modern problems lie at the intersection of strong correlations and quantum information where highly entangled phases of matter are the most difficult to solve both analytically and computationally. The overarching aim of this thesis is to advance our understanding of strongly correlated materials in light of advanced, microscopic measurement techniques, capable of imaging and manipulating single qubits and measuring fascinating physics such as quantum entanglement. We begin our study with the Fermi-Hubbard model, a theoretical model that captures the insulating and conducting phases of high-temperature superconducting materials, and we end our discussion by characterizing novel quantum phases and dynamics realized on cutting-edge quantum simulation platforms. Our first focus is on the repulsive Fermi-Hubbard model. We elucidate the mechanism by which a Mott insulator transforms into a non-Fermi liquid metal upon increasing disorder at half filling. By correlating maps of the local density of states, the local magnetization, and the local bond conductivity, we find a collapse of the Mott gap toward a V-shape pseudogapped density of states that occurs concomitantly with the decrease of magnetism around the highly disordered sites, while the electronic bond conductivity increases. We propose that these metallic regions percolate to form an emergent non-Fermi liquid phase with a conductivity that increases with temperature. Our results provide one of the first microscopic investigations of dynamical response and how these two phases (correlated metal and Mott insulator) coexist microscopically and lead to an overall macroscopic phase transition. Our work provides novel predictions for electron conductivity measured via local microwave impedance combined with charge and spin local spectroscopies. Expanding beyond the ground state properties of interacting matter, revolutionary quantum simulation experiments provide access to new regimes of quantum matter such as dynamical transitions and steady states in nonequilibrium conditions. This allows us to explore the most mind-boggling properties of interacting quantum systems: entanglement. In our first venture exploring the field of nonequilibrium quantum dynamics, we bridge foundational atomic, molecular, and optical (AMO) and condensed matter models. We investigate competing entanglement dynamics in an Ising-spin chain coupled to an external central ancilla qudit. In studying the real-time behavior following a quench from an unentangled spin-ancilla state, we find that the ancilla entanglement entropy tracks the dynamical phase transition in the underlying spin system. In this composite setting, purely spin-spin entanglement metrics such as mutual information and quantum Fisher information (QFI) decay as the ancilla entanglement entropy grows. We define multipartite entanglement loss (MEL) as the difference between collective magnetic fluctuations and QFI, which is zero in the pure spin chain limit. MEL directly quantifies the ancilla's effect on the development of spin-spin entanglement. One of our central results is that we find MEL is proportional to the exponential of entanglement entropy in real-time. Our results provide a platform for exploring composite system entanglement dynamics and suggest that MEL serves as a quantitative estimate of information entropy shared between collective spins and the ancilla qudit. Our results present a new framework that connects physical spin-fluctuations, QFI, and bipartite entanglement entropy between collective quantum systems. We reduce the qudit/bosonic environment to a single (central) qubit as to investigate the scrambling capacity added by a simple c-qubit. We present the novel ring-star Ising model as a bridge between fast-slow scrambling: a locally interacting spin-1/2 system uniformly coupled to a central qubit vertex. Each spin becomes next-nearest neighbor to all others through the c-qubit, where stronger central coupling continuously degrades any sense of locality and achieves effective all-to-all interactions. Meanwhile, the central qubit adds two level structure to all previous eigenstates in the spectrum. We study operator and entanglement dynamics in a nonintegrable ring-star, spin-1/2 Ising model with tunable central spin coupling. As the interaction with the c-spin increases across all sites, we find a surprising transition from super-ballistic scrambling and information growth to continuously restricted sub-ballistic entanglement and increasingly inhibited operator growth. This slow growth occurs on intermediate timescales that extend exponentially with increasing coupling, indicative of logarithmic entanglement growth. We provide exact dynamics of small systems working with non-equilibrium, effective infinite temperature states, and additionally contribute analytic early-time expansions that support the observed rapid scrambling to quantum Zeno-like crossover. Finally, we apply the properties of entanglement to highlight numerically approximate methods for simulating quantum and semiclassical systems. When entanglement slowly develops locally, tensor network methods allow for efficient simulation of the minimal Hilbert space required to store the quantum wavefunction evolving under Schrodinger dynamics or quantum operators under Heisenberg evolution. In the limit of long-range interactions, the system is increasingly semiclassical where the wavefunction spreads rapidly, but the full quantum Hilbert space approaches proximate conservation of collective observables. Here we review tensor network and semiclassical numerical algorithms and provide a brief discussion on applying them to simulate the quench dynamics of the Heisenberg model. We highlight the regimes where we expect them to be accurate and the intermediate regions where the two become approximate from different limits on the range of interaction.

Download or read book Random Operators written by Michael Aizenman and published by American Mathematical Soc.. This book was released on 2015-12-11 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the mathematical theory of disorder effects on quantum spectra and dynamics. Topics covered range from the basic theory of spectra and dynamics of self-adjoint operators through Anderson localization--presented here via the fractional moment method, up to recent results on resonant delocalization. The subject's multifaceted presentation is organized into seventeen chapters, each focused on either a specific mathematical topic or on a demonstration of the theory's relevance to physics, e.g., its implications for the quantum Hall effect. The mathematical chapters include general relations of quantum spectra and dynamics, ergodicity and its implications, methods for establishing spectral and dynamical localization regimes, applications and properties of the Green function, its relation to the eigenfunction correlator, fractional moments of Herglotz-Pick functions, the phase diagram for tree graph operators, resonant delocalization, the spectral statistics conjecture, and related results. The text incorporates notes from courses that were presented at the authors' respective institutions and attended by graduate students and postdoctoral researchers.

Download or read book Emergent Phenomena in Correlated Matter written by Eva Pavarini and published by Forschungszentrum Jülich. This book was released on 2013 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Simulating Strongly Interacting Quantum Spin Systems written by Stefanie Czischek and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Introduction to Quantum Spin Systems written by John B. Parkinson and published by Springer Science & Business Media. This book was released on 2010-09-20 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Simulating Strongly Interacting Quantum Spin Systems written by Stefanie Czischek and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Irreversible Quantum Dynamics written by Fabio Benatti and published by Springer. This book was released on 2008-01-11 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea of editing the present volume in the Lecture Notes in Physics series arosewhileorganizingthe“ConferenceonIrreversibleQuantumDynamics”that took place at The Abdus Salam International Center for Theoretical Physics, Trieste, Italy, from July 29 to August 2, 2002. The aim of the Conference was to bring together di?erent groups of - searcherswhoseinterestsandpursuitsinvolveirreversibilityandtimeasymmetry in quantum mechanics. The Conference promoted open and in-depth exchanges of di?erent points of view, concerning both the content and character of qu- tum irreversibility and the methodologies used to study it. The following main themes were addressed: • Theoretical Aspects of Quantum Irreversible Dynamics • Open Quantum Systems and Applications • Foundational Aspects of Irreversible Quantum Dynamics • Asymmetric Time Evolution and Resonances Eachthemewasreviewedbyanexpertinthe?eld,accompaniedbymorespeci?c, research-like shorter talks. The whole topic of quantum irreversibility in all its manifold aspects has always raised a lot of interest, starting with the description of unstable systems in quantum mechanics and the issue of quantum measurement. Further, in - cent years a boost of activity concerning noise, dissipation and open systems has been prompted by the fast developing ?eld of quantum communication and information theory. These considerations motivated the editors to put together a volume that tries to summarize the present day status of the research in the ?eld, with the aim of providing the reader with an accessible and exhaustive introduction to it.

Download or read book First principle Approaches to Strongly Correlated Quantum Spin Systems written by Yuan Huang and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: My Ph.D. research focuses on the numerical study of two quantum spin systems, one is the square-lattice Heisenberg antiferromagnet with ring-exchange interaction at the Neel to valence-bond solid state transition, which is proposed to be described by the theory of deconfined criticality; the other is the highly frustrated pyrochlore Heisenberg antiferromagnet. Both systems are known as prototypical candidates for the exotic spin-liquid state with emergent fractionalized excitations and gauge structure. Regarding the long standing controversy of deconfined criticality, our results conclude that the deconfined critical theory capture the essence of the Neel to valence-bond solid state transition at least at intermediate scales of distances, and also suggest that both the deconfined critical point and the Neel to valence-bond solid state transition are weak first-order transitions. In the frustrated pyrochlore Heisenberg antiferromagnet, we found a wide cooperative paramagnetic temperature regime where the system is in an emergent thermal spin-ice state. The conclusion is drawn by a remarkably accurate microscopic correspondence for static structure factor between the quantum Heisenberg model and its classical counterparts. An analysis for the dynamic structure factor obtained by the analytic continuation of numerical data is also performed, showing a result consistent with diffusive spinon dynamics of certain special modes.

Download or read book Frustrated Spin Systems written by H. T. Diep and published by World Scientific. This book was released on 2013 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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."

Download or read book Entanglement Properties of Strongly Correlated Spin Systems written by and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Entanglement Properties of Strongly Correlated Spin Systems written by Moritz Emil Reuter and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Quantum Information Theory written by Mark Wilde and published by Cambridge University Press. This book was released on 2013-04-18 with total page 673 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained, graduate-level textbook that develops from scratch classical results as well as advances of the past decade.

Download or read book Holographic Entanglement Entropy written by Mukund Rangamani and published by Springer. This book was released on 2017-05-08 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Physics of Quantum Mechanics written by James Binney and published by Oxford University Press, USA. This book was released on 2013-12 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title gives students a good understanding of how quantum mechanics describes the material world. The text stresses the continuity between the quantum world and the classical world, which is merely an approximation to the quantum world.

Download or read book Introduction to Frustrated Magnetism written by Claudine Lacroix and published by Springer Science & Business Media. This book was released on 2011-01-12 with total page 682 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.