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Author: Joel Pérez Díaz Publisher: ISBN: Category : Languages : en Pages :
Book Description
A Neural Network is trained to classify Mott Insulator and Superfluid phases in an optical lattice using data generated with Diffusion Monte Carlo algorithms (DMC). The trained model is used to predict the phase transition and its dependence with different training parameters is studied. The study of this dependence shows the existence of optimal training and simulation parameters, which cannot be used due to computational limitations. This prevents to calculate the phase transition diagram consistent with other theoretical and experimental results.
Author: Joel Pérez Díaz Publisher: ISBN: Category : Languages : en Pages :
Book Description
A Neural Network is trained to classify Mott Insulator and Superfluid phases in an optical lattice using data generated with Diffusion Monte Carlo algorithms (DMC). The trained model is used to predict the phase transition and its dependence with different training parameters is studied. The study of this dependence shows the existence of optimal training and simulation parameters, which cannot be used due to computational limitations. This prevents to calculate the phase transition diagram consistent with other theoretical and experimental results.
Author: Laura Malo Roset Publisher: ISBN: Category : Languages : en Pages :
Book Description
In the past years Machine Learning has shown to be a useful tool in quantum many-body physics to detect phase transitions. Being able to identify phases via machine learning introduces the question of how did the algorithm learn to classify them, and thus how to interpret the model?s prediction. In this thesis we present a study of the transition from a normal insulator to a topological insulator. We study this quantum phase transition in the framework of the Su-Schrie?er-Heeger model. In the area of Deep Learning, we introduce two models, a normal convolutional neural network and a model based on deep residual learning. In particular, we focus on the interpretability of the model and its prediction by generating class activation maps (CAM) using a global average pooling (GAP) layer. We show the application of this technique by applying it on the model without disorder and with disorder. Here we give further analysis of the detection of states using transfer learning from no disordered to disordered systems. We conclude that the neural network is able to detect edge states when there is no disorder but unable to distinguish between edge states and Anderson localized states when disorder is introduced.
Author: Wenjian Hu Publisher: ISBN: 9780355969696 Category : Languages : en Pages :
Book Description
In condensed matter physics, researchers study the physical properties of condensed phases of matter, theoretically or experimentally. The fundamentally appealing topic in this research area is how to classify phases of matter and identify phase transitions between them.Different from traditional theoretical or experimental approaches, which relies on either complicated mathematical formulation or equally complex experimental equipment, Monte Carlo based stochastic methods, which are often treated as "computer experiments", introduce a relatively "cheap" but effective approach to study phases and phase transitions. In this dissertation, we employ the classical Monte Carlo simulation, which utilizes the Metropolis algorithm to evolve system configurations, and also the determinant quantum Monte Carlo simulation to study phases and phase transitions of model Hamiltonians, such as the Hubbard model, and the periodic Anderson model (PAM). In the 21st century, data driven machine learning techniques have proven to be an another research "engine" for detecting phases and phase transitions. In this dissertation, I explore potential usages of unsupervised machine learning techniques in phase transition. Specifically, I leverage the principal component analysis (PCA) to extract internal structures, which are fully reflected in leading principal components, of Monte Carlo generated configurations, and then quantify obtained principal components to distinguish phases and phase transitions. This technique is applied to study model Hamiltonians, such as the Ising model, the XY model, the Hubbard model and the PAM. The exact organization of this dissertation is as follows: In chapter 1, I first introduce basic concepts of phase transitions and related model Hamiltonians. In chapter 2, I talk about a variety of methodologies utilized. In chapter 3, I present studies of phase transitions in a spin-fermion model. In chapter 4, I explore phase diagrams of the PAM coupled with an additional layer of metal. In chapter 5 and 6, I discuss how to apply machine learning techniques, especially PCA, to distinguish phases and detect phase transitions in classical and quantum model Hamiltonians. In chapter 7, I summarize previous chapters and discuss potential future directions.
Author: Lincoln Carr Publisher: CRC Press ISBN: 1439802610 Category : Science Languages : en Pages : 754
Book Description
Quantum phase transitions (QPTs) offer wonderful examples of the radical macroscopic effects inherent in quantum physics: phase changes between different forms of matter driven by quantum rather than thermal fluctuations, typically at very low temperatures. QPTs provide new insight into outstanding problems such as high-temperature superconductivit
Author: Sei Suzuki Publisher: Springer ISBN: 9783642330407 Category : Science Languages : en Pages : 403
Book Description
Quantum phase transitions, driven by quantum fluctuations, exhibit intriguing features offering the possibility of potentially new applications, e.g. in quantum information sciences. Major advances have been made in both theoretical and experimental investigations of the nature and behavior of quantum phases and transitions in cooperatively interacting many-body quantum systems. For modeling purposes, most of the current innovative and successful research in this field has been obtained by either directly or indirectly using the insights provided by quantum (or transverse field) Ising models because of the separability of the cooperative interaction from the tunable transverse field or tunneling term in the relevant Hamiltonian. Also, a number of condensed matter systems can be modeled accurately in this approach, hence granting the possibility to compare advanced models with actual experimental results. This work introduces these quantum Ising models and analyses them both theoretically and numerically in great detail. With its tutorial approach the book addresses above all young researchers who wish to enter the field and are in search of a suitable and self-contained text, yet it will also serve as a valuable reference work for all active researchers in this area.
Author: Subir Sachdev Publisher: Cambridge University Press ISBN: 9780521514682 Category : Science Languages : en Pages : 517
Book Description
Describing the physical properties of quantum materials near critical points with long-range many-body quantum entanglement, this book introduces readers to the basic theory of quantum phases, their phase transitions and their observable properties. This second edition begins with a new section suitable for an introductory course on quantum phase transitions, assuming no prior knowledge of quantum field theory. It also contains several new chapters to cover important recent advances, such as the Fermi gas near unitarity, Dirac fermions, Fermi liquids and their phase transitions, quantum magnetism, and solvable models obtained from string theory. After introducing the basic theory, it moves on to a detailed description of the canonical quantum-critical phase diagram at non-zero temperatures. Finally, a variety of more complex models are explored. This book is ideal for graduate students and researchers in condensed matter physics and particle and string theory.
Author: Elena V. Levchenko Publisher: Springer Nature ISBN: 3030377903 Category : Technology & Engineering Languages : en Pages : 292
Book Description
This book provides a unique and comprehensive overview of the latest advances, challenges and accomplishments in the rapidly growing field of theoretical and computational materials science. Today, an increasing number of industrial communities rely more and more on advanced atomic-scale methods to obtain reliable predictions of materials properties, complement qualitative experimental analyses and circumvent experimental difficulties. The book examines some of the latest and most advanced simulation techniques currently available, as well as up-to-date theoretical approaches adopted by a selected panel of twelve international research teams. It covers a wide range of novel and advanced materials, exploring their structural, elastic, optical, mass and electronic transport properties. The cutting-edge techniques presented appeal to physicists, applied mathematicians and engineers interested in advanced simulation methods in materials science. The book can also be used as additional literature for undergraduate and postgraduate students with majors in physics, chemistry, applied mathematics and engineering.
Author: Joel Pérez Díaz
Author: Joel Pérez Díaz
Author: Laura Malo Roset
Author: Wenjian Hu
Author: Lincoln Carr
Author: Sei Suzuki
Author: Roman Orus Lacort
Author: Roman Orus Lacort
Author: 
Author: Subir Sachdev
Author: Elena V. Levchenko