Physics and Mathematics of Quantum Many-Body Systems
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Beschreibung
This book is a self-contained advanced textbook on the mathematical-physical aspects of quantum many-body systems, which begins with a pedagogical presentation of the necessary background information before moving on to subjects of active research, including topological phases of matter.
The book explores in detail selected topics in quantum spin systems and lattice electron systems, namely, long-range order and spontaneous symmetry breaking in the antiferromagnetic Heisenberg model in two or higher dimensions (Part I), the Haldane phenomenon in antiferromagnetic quantum spin chains and related topics in topological phases of quantum matter (Part II), and the origin of magnetism in various versions of the Hubbard model (Part III). Each of these topics represents certain nontrivial phenomena or features that are invariably encountered in a variety of quantum many-body systems, including quantum field theory, condensed matter systems, cold atoms, and artificial quantum systems designed for future quantum computers. The book’s main focus is on universal properties of quantum many-body systems.
The book includes roughly 50 problems with detailed solutions. The reader only requires elementary linear algebra and calculus to comprehend the material and work through the problems. Given its scope and format, the book is suitable both for self-study and as a textbook for graduate or advanced undergraduate classes.
This book is a self-contained advanced textbook on the mathematical-physical aspects of quantum many-body systems, which begins with a pedagogical presentation of the necessary background information before moving on to subjects of active research, including topological phases of matter.
The book explores in detail selected topics in quantum spin systems and lattice electron systems, namely, long-range order and spontaneous symmetry breaking in the antiferromagnetic Heisenberg model in two or higher dimensions (Part I), Haldane phenomena in antiferromagnetic quantum spin chains and related topics in topological phases of quantum matter (Part II), and the origin of magnetism in various versions of the Hubbard model (Part III). Each of these topics represents certain nontrivial phenomena or features that are invariably encountered in a variety of quantum many-body systems, including quantum field theory, condensed matter systems, cold atoms, and artificial quantum systems designed for future quantum computers. The book’s main focus is on universal properties of quantum many-body systems.
The book includes roughly 50 problems with detailed solutions. The reader only requires elementary linear algebra and calculus to comprehend the material and work through the problems. Given its scope and format, the book is suitable both for self-study and as a textbook for graduate or advanced undergraduate classes.
Provides the first comprehensive and detailed review of the Haldane phenomenon, a typical example of the “topological phase of matter,” and the subject of the 2016 Nobel Prize in Physics Discusses some of the most important universal properties of quantum many-body systems, which can be observed in a broad range of physical systems Begins with a pedagogical presentation of the necessary background information and leads the reader to subjects of active research, such as topological phases of matter Detailed and self-contained; all important results are carefully proved, using only undergraduate mathematics Provides a bridge between researchers in various fields, including condensed matter physics, high-energy physics, quantum information science, and mathematics
Autor*in
Hal Tasaki
Themen in »Physics and Mathematics of Quantum Many-Body Systems«
Quantum spin systems Symmetry-protected topological phases Ising model Heisenberg antiferromagnet Affleck-Kennedy-Lieb-Tasaki model Hubbard model Haldane phenomena Topological phase of matter Haldane conjecture Spontaneous symmetry breaking