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Geometrically Constructed Markov Chain Monte Carlo Study of Quantum Spin-phonon Complex Systems

2013-11-05 Science
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Release : 2013-11-05
Genre : Science
Kind : eBook
Book Rating : 174/5 ( reviews)

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Book Synopsis Geometrically Constructed Markov Chain Monte Carlo Study of Quantum Spin-phonon Complex Systems by : Hidemaro Suwa

Download or read book Geometrically Constructed Markov Chain Monte Carlo Study of Quantum Spin-phonon Complex Systems written by Hidemaro Suwa. This book was released on 2013-11-05. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, novel Monte Carlo methods for precisely calculating the critical phenomena of the effectively frustrated quantum spin system are developed and applied to the critical phenomena of the spin-Peierls systems. Three significant methods are introduced for the first time: a new optimization algorithm of the Markov chain transition kernel based on the geometric weight-allocation approach, the extension of the worm (directed-loop) algorithm to nonconserved particles, and the combination with the level spectroscopy. Utilizing these methods, the phase diagram of the one-dimensional XXZ spin-Peierls system is elucidated. Furthermore, the multi-chain and two-dimensional spin-Peierls systems with interchain lattice interaction are investigated. The unbiased simulation shows that the interesting quantum phase transition between the 1D-like liquid phase and the macroscopically-degenerated dimer phase occurs on the fully-frustrated parameter line that separates the doubly-degenerated dimer phases in the two-dimensional phase diagram. The spin-phonon interaction in the spin-Peierls system introduces the spin frustration, which usually hinders the quantum Monte Carlo analysis, owing to the notorious negative sign problem. In this thesis, the author has succeeded in precisely calculating the critical phenomena of the effectively frustrated quantum spin system by means of the quantum Monte Carlo method without the negative sign.

Magnetic Field Effects in Low-Dimensional Quantum Magnets

2018-11-28 Science
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Release : 2018-11-28
Genre : Science
Kind : eBook
Book Rating : 032/5 ( reviews)

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Book Synopsis Magnetic Field Effects in Low-Dimensional Quantum Magnets by : Adam Iaizzi

Download or read book Magnetic Field Effects in Low-Dimensional Quantum Magnets written by Adam Iaizzi. This book was released on 2018-11-28. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is a tour-de-force combination of analytic and computational results clarifying and resolving important questions about the nature of quantum phase transitions in one- and two-dimensional magnetic systems. The author presents a comprehensive study of a low-dimensional spin-half quantum antiferromagnet (the J-Q model) in the presence of a magnetic field in both one and two dimensions, demonstrating the causes of metamagnetism in such systems and providing direct evidence of fractionalized excitations near the deconfined quantum critical point. In addition to describing significant new research results, this thesis also provides the non-expert with a clear understanding of the nature and importance of computational physics and its role in condensed matter physics as well as the nature of phase transitions, both classical and quantum. It also contains an elegant and detailed but accessible summary of the methods used in the thesis—exact diagonalization, Monte Carlo, quantum Monte Carlo and the stochastic series expansion—that will serve as a valuable pedagogical introduction to students beginning in this field.

Journal of the Physical Society of Japan

2017 Physics
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Release : 2017
Genre : Physics
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Journal of the Physical Society of Japan by :

Download or read book Journal of the Physical Society of Japan written by . This book was released on 2017. Available in PDF, EPUB and Kindle. Book excerpt:

Markov Chain Monte Carlo Methods in Quantum Field Theories

2020-04-16 Science
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Release : 2020-04-16
Genre : Science
Kind : eBook
Book Rating : 444/5 ( reviews)

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Book Synopsis Markov Chain Monte Carlo Methods in Quantum Field Theories by : Anosh Joseph

Download or read book Markov Chain Monte Carlo Methods in Quantum Field Theories written by Anosh Joseph. This book was released on 2020-04-16. Available in PDF, EPUB and Kindle. Book excerpt: This primer is a comprehensive collection of analytical and numerical techniques that can be used to extract the non-perturbative physics of quantum field theories. The intriguing connection between Euclidean Quantum Field Theories (QFTs) and statistical mechanics can be used to apply Markov Chain Monte Carlo (MCMC) methods to investigate strongly coupled QFTs. The overwhelming amount of reliable results coming from the field of lattice quantum chromodynamics stands out as an excellent example of MCMC methods in QFTs in action. MCMC methods have revealed the non-perturbative phase structures, symmetry breaking, and bound states of particles in QFTs. The applications also resulted in new outcomes due to cross-fertilization with research areas such as AdS/CFT correspondence in string theory and condensed matter physics. The book is aimed at advanced undergraduate students and graduate students in physics and applied mathematics, and researchers in MCMC simulations and QFTs. At the end of this book the reader will be able to apply the techniques learned to produce more independent and novel research in the field.

Quantum Monte Carlo Methods In Condensed Matter Physics

1993-12-30 Science
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Release : 1993-12-30
Genre : Science
Kind : eBook
Book Rating : 337/5 ( reviews)

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Book Synopsis Quantum Monte Carlo Methods In Condensed Matter Physics by : Masuo Suzuki

Download or read book Quantum Monte Carlo Methods In Condensed Matter Physics written by Masuo Suzuki. This book was released on 1993-12-30. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews recent developments of quantum Monte Carlo methods and some remarkable applications to interacting quantum spin systems and strongly correlated electron systems. It contains twenty-two papers by thirty authors. Some of the features are as follows. The first paper gives the foundations of the standard quantum Monte Carlo method, including some recent results on higher-order decompositions of exponential operators and ordered exponentials. The second paper presents a general review of quantum Monte Carlo methods used in the present book. One of the most challenging problems in the field of quantum Monte Carlo techniques, the negative-sign problem, is also discussed and new methods proposed to partially overcome it. In addition, low-dimensional quantum spin systems are studied. Some interesting applications of quantum Monte Carlo methods to fermion systems are also presented to investigate the role of strong correlations and fluctuations of electrons and to clarify the mechanism of high-Tc superconductivity. Not only thermal properties but also quantum-mechanical ground-state properties have been studied by the projection technique using auxiliary fields. Further, the Haldane gap is confirmed by numerical calculations. Active researchers in the forefront of condensed matter physics as well as young graduate students who want to start learning the quantum Monte Carlo methods will find this book useful.

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