Topology In Condensed Matter An Introduction

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Topology In Condensed Matter: An Introduction

Miguel A N Araujo,Pedro Sacramento
Topology In Condensed Matter An Introduction Book PDF

Author : Miguel A N Araujo,Pedro Sacramento
Publisher : World Scientific
Page : 276 pages
File Size : 46,9 Mb
Release : 2021-05-19
Category : Science
ISBN : 9789811237232

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Topology In Condensed Matter: An Introduction by Miguel A N Araujo,Pedro Sacramento Pdf

This text serves as a pedagogical introduction to the theoretical concepts on application of topology in condensed matter systems. It covers an introduction to basic concepts of topology, emphasizes the relation of geometric concepts such as the Berry phase to topology, having in mind applications in condensed matter. In addition to describing two basic systems such as topological insulators and topological superconductors, it also reviews topological spin systems and photonic systems. It also describes the use of quantum information concepts in the context of topological phases and phase transitions, and the effect of non-equilibrium perturbations on topological systems.This book provides a comprehensive introduction to topological insulators, topological superconductors and topological semimetals. It includes all the mathematical background required for the subject. There are very few books with such a coverage in the market.

Topology in Condensed Matter

Michael I. Monastyrsky
Topology in Condensed Matter Book PDF

Author : Michael I. Monastyrsky
Publisher : Springer Science & Business Media
Page : 263 pages
File Size : 54,8 Mb
Release : 2006-02-04
Category : Science
ISBN : 9783540312642

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Topology in Condensed Matter by Michael I. Monastyrsky Pdf

This book reports new results in condensed matter physics for which topological methods and ideas are important. It considers, on the one hand, recently discovered systems such as carbon nanocrystals and, on the other hand, new topological methods used to describe more traditional systems such as the Fermi surfaces of normal metals, liquid crystals and quasicrystals. The authors of the book are renowned specialists in their fields and present the results of ongoing research, some of it obtained only very recently and not yet published in monograph form.

A Brief Introduction to Topology and Differential Geometry in Condensed Matter Physics

Antonio Sergio Teixeira Pires
A Brief Introduction to Topology and Differential Geometry in Condensed Matter Physics Book PDF

Author : Antonio Sergio Teixeira Pires
Publisher : Morgan & Claypool Publishers
Page : 171 pages
File Size : 50,8 Mb
Release : 2019-03-21
Category : Science
ISBN : 9781643273747

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A Brief Introduction to Topology and Differential Geometry in Condensed Matter Physics by Antonio Sergio Teixeira Pires Pdf

In the last years there have been great advances in the applications of topology and differential geometry to problems in condensed matter physics. Concepts drawn from topology and geometry have become essential to the understanding of several phenomena in the area. Physicists have been creative in producing models for actual physical phenomena which realize mathematically exotic concepts and new phases have been discovered in condensed matter in which topology plays a leading role. An important classification paradigm is the concept of topological order, where the state characterizing a system does not break any symmetry, but it defines a topological phase in the sense that certain fundamental properties change only when the system passes through a quantum phase transition. The main purpose of this book is to provide a brief, self-contained introduction to some mathematical ideas and methods from differential geometry and topology, and to show a few applications in condensed matter. It conveys to physicists the basis for many mathematical concepts, avoiding the detailed formality of most textbooks.

Topology and Condensed Matter Physics

Somendra Mohan Bhattacharjee,Mahan Mj,Abhijit Bandyopadhyay
Topology and Condensed Matter Physics Book PDF

Author : Somendra Mohan Bhattacharjee,Mahan Mj,Abhijit Bandyopadhyay
Publisher : Springer
Page : 507 pages
File Size : 47,5 Mb
Release : 2017-12-20
Category : Science
ISBN : 9789811068416

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Topology and Condensed Matter Physics by Somendra Mohan Bhattacharjee,Mahan Mj,Abhijit Bandyopadhyay Pdf

This book introduces aspects of topology and applications to problems in condensed matter physics. Basic topics in mathematics have been introduced in a form accessible to physicists, and the use of topology in quantum, statistical and solid state physics has been developed with an emphasis on pedagogy. The aim is to bridge the language barrier between physics and mathematics, as well as the different specializations in physics. Pitched at the level of a graduate student of physics, this book does not assume any additional knowledge of mathematics or physics. It is therefore suited for advanced postgraduate students as well. A collection of selected problems will help the reader learn the topics on one's own, and the broad range of topics covered will make the text a valuable resource for practising researchers in the field. The book consists of two parts: one corresponds to developing the necessary mathematics and the other discusses applications to physical problems. The section on mathematics is a quick, but more-or-less complete, review of topology. The focus is on explaining fundamental concepts rather than dwelling on details of proofs while retaining the mathematical flavour. There is an overview chapter at the beginning and a recapitulation chapter on group theory. The physics section starts with an introduction and then goes on to topics in quantum mechanics, statistical mechanics of polymers, knots, and vertex models, solid state physics, exotic excitations such as Dirac quasiparticles, Majorana modes, Abelian and non-Abelian anyons. Quantum spin liquids and quantum information-processing are also covered in some detail.

Topological Phases of Matter

Roderich Moessner,Joel E. Moore
Topological Phases of Matter Book PDF

Author : Roderich Moessner,Joel E. Moore
Publisher : Cambridge University Press
Page : 393 pages
File Size : 55,5 Mb
Release : 2021-04-29
Category : Mathematics
ISBN : 9781107105539

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Topological Phases of Matter by Roderich Moessner,Joel E. Moore Pdf

This important graduate level text unites the physical mechanisms behind the phenomena of topological matter within a theoretical framework.

Topological Insulators

Shun-Qing Shen
Topological Insulators Book PDF

Author : Shun-Qing Shen
Publisher : Springer Science & Business Media
Page : 225 pages
File Size : 44,5 Mb
Release : 2013-01-11
Category : Technology & Engineering
ISBN : 9783642328589

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Topological Insulators by Shun-Qing Shen Pdf

Topological insulators are insulating in the bulk, but process metallic states present around its boundary owing to the topological origin of the band structure. The metallic edge or surface states are immune to weak disorder or impurities, and robust against the deformation of the system geometry. This book, the first of its kind on topological insulators, presents a unified description of topological insulators from one to three dimensions based on the modified Dirac equation. A series of solutions of the bound states near the boundary are derived, and the existing conditions of these solutions are described. Topological invariants and their applications to a variety of systems from one-dimensional polyacetalene, to two-dimensional quantum spin Hall effect and p-wave superconductors, and three-dimensional topological insulators and superconductors or superfluids are introduced, helping readers to better understand this fascinating new field. This book is intended for researchers and graduate students working in the field of topological insulators and related areas. Shun-Qing Shen is a Professor at the Department of Physics, the University of Hong Kong, China.

Topological Insulators and Topological Superconductors

B. Andrei Bernevig
Topological Insulators and Topological Superconductors Book PDF

Author : B. Andrei Bernevig
Publisher : Princeton University Press
Page : 264 pages
File Size : 44,5 Mb
Release : 2013-04-07
Category : Science
ISBN : 9781400846733

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Topological Insulators and Topological Superconductors by B. Andrei Bernevig Pdf

This graduate-level textbook is the first pedagogical synthesis of the field of topological insulators and superconductors, one of the most exciting areas of research in condensed matter physics. Presenting the latest developments, while providing all the calculations necessary for a self-contained and complete description of the discipline, it is ideal for graduate students and researchers preparing to work in this area, and it will be an essential reference both within and outside the classroom. The book begins with simple concepts such as Berry phases, Dirac fermions, Hall conductance and its link to topology, and the Hofstadter problem of lattice electrons in a magnetic field. It moves on to explain topological phases of matter such as Chern insulators, two- and three-dimensional topological insulators, and Majorana p-wave wires. Additionally, the book covers zero modes on vortices in topological superconductors, time-reversal topological superconductors, and topological responses/field theory and topological indices. The book also analyzes recent topics in condensed matter theory and concludes by surveying active subfields of research such as insulators with point-group symmetries and the stability of topological semimetals. Problems at the end of each chapter offer opportunities to test knowledge and engage with frontier research issues. Topological Insulators and Topological Superconductors will provide graduate students and researchers with the physical understanding and mathematical tools needed to embark on research in this rapidly evolving field.

A Short Course on Topological Insulators

János K. Asbóth,László Oroszlány,András Pályi Pályi
A Short Course on Topological Insulators Book PDF

Author : János K. Asbóth,László Oroszlány,András Pályi Pályi
Publisher : Springer
Page : 166 pages
File Size : 55,9 Mb
Release : 2016-02-22
Category : Science
ISBN : 9783319256078

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A Short Course on Topological Insulators by János K. Asbóth,László Oroszlány,András Pályi Pályi Pdf

This course-based primer provides newcomers to the field with a concise introduction to some of the core topics in the emerging field of topological insulators. The aim is to provide a basic understanding of edge states, bulk topological invariants, and of the bulk--boundary correspondence with as simple mathematical tools as possible. The present approach uses noninteracting lattice models of topological insulators, building gradually on these to arrive from the simplest one-dimensional case (the Su-Schrieffer-Heeger model for polyacetylene) to two-dimensional time-reversal invariant topological insulators (the Bernevig-Hughes-Zhang model for HgTe). In each case the discussion of simple toy models is followed by the formulation of the general arguments regarding topological insulators. The only prerequisite for the reader is a working knowledge in quantum mechanics, the relevant solid state physics background is provided as part of this self-contained text, which is complemented by end-of-chapter problems.

Introduction to Topological Quantum Matter & Quantum Computation

Tudor D. Stanescu
Introduction to Topological Quantum Matter Quantum Computation Book PDF

Author : Tudor D. Stanescu
Publisher : CRC Press
Page : 380 pages
File Size : 44,8 Mb
Release : 2016-12-19
Category : Science
ISBN : 9781482245943

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Introduction to Topological Quantum Matter & Quantum Computation by Tudor D. Stanescu Pdf

What is "topological" about topological quantum states? How many types of topological quantum phases are there? What is a zero-energy Majorana mode, how can it be realized in a solid state system, and how can it be used as a platform for topological quantum computation? What is quantum computation and what makes it different from classical computation? Addressing these and other related questions, Introduction to Topological Quantum Matter & Quantum Computation provides an introduction to and a synthesis of a fascinating and rapidly expanding research field emerging at the crossroads of condensed matter physics, mathematics, and computer science. Providing the big picture, this book is ideal for graduate students and researchers entering this field as it allows for the fruitful transfer of paradigms and ideas amongst different areas, and includes many specific examples to help the reader understand abstract and sometimes challenging concepts. It explores the topological quantum world beyond the well-known topological insulators and superconductors and emphasizes the deep connections with quantum computation. It addresses key principles behind the classification of topological quantum phases and relevant mathematical concepts and discusses models of interacting and noninteracting topological systems, such as the torric code and the p-wave superconductor. The book also covers the basic properties of anyons, and aspects concerning the realization of topological states in solid state structures and cold atom systems. Quantum computation is also presented using a broad perspective, which includes fundamental aspects of quantum mechanics, such as Bell's theorem, basic concepts in the theory of computation, such as computational models and computational complexity, examples of quantum algorithms, and elements of classical and quantum information theory.

Quantum Field Theory and Topology

Albert S. Schwarz
Quantum Field Theory and Topology Book PDF

Author : Albert S. Schwarz
Publisher : Springer Science & Business Media
Page : 277 pages
File Size : 50,5 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9783662029435

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Quantum Field Theory and Topology by Albert S. Schwarz Pdf

In recent years topology has firmly established itself as an important part of the physicist's mathematical arsenal. It has many applications, first of all in quantum field theory, but increasingly also in other areas of physics. The main focus of this book is on the results of quantum field theory that are obtained by topological methods. Some aspects of the theory of condensed matter are also discussed. Part I is an introduction to quantum field theory: it discusses the basic Lagrangians used in the theory of elementary particles. Part II is devoted to the applications of topology to quantum field theory. Part III covers the necessary mathematical background in summary form. The book is aimed at physicists interested in applications of topology to physics and at mathematicians wishing to familiarize themselves with quantum field theory and the mathematical methods used in this field. It is accessible to graduate students in physics and mathematics.

Quantum Field Theory and Condensed Matter

Ramamurti Shankar
Quantum Field Theory and Condensed Matter Book PDF

Author : Ramamurti Shankar
Publisher : Unknown
Page : 537 pages
File Size : 42,9 Mb
Release : 2017
Category : Condensed matter
ISBN : 9781108363464

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Quantum Field Theory and Condensed Matter by Ramamurti Shankar Pdf

Providing a broad review of many techniques and their application to condensed matter systems, this book begins with a review of thermodynamics and statistical mechanics, before moving onto real and imaginary time path integrals and the link between Euclidean quantum mechanics and statistical mechanics. A detailed study of the Ising, gauge-Ising and XY models is included. The renormalization group is developed and applied to critical phenomena, Fermi liquid theory and the renormalization of field theories. Next, the book explores bosonization and its applications to one-dimensional fermionic systems and the correlation functions of homogeneous and random-bond Ising models. It concludes with Bohm-Pines and Chern-Simons theories applied to the quantum Hall effect. Introducing the reader to a variety of techniques, it opens up vast areas of condensed matter theory for both graduate students and researchers in theoretical, statistical and condensed matter physics.

Topological Disorder in Condensed Matter

F. Yonezawa,T. Ninomiya
Topological Disorder in Condensed Matter Book PDF

Author : F. Yonezawa,T. Ninomiya
Publisher : Springer Science & Business Media
Page : 262 pages
File Size : 43,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642821042

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Topological Disorder in Condensed Matter by F. Yonezawa,T. Ninomiya Pdf

This volume contains papers presented at the Fifth Taniguchi Symposium on the Theory of Condensed Matter, which was held between 2-5 November, 1982, at Shimoda, Japan. The topic of the Symposium was "Topological Disorder in Condensed Matter. " The objective of the Taniguchi Symposium is to encourage activity in those fields of research not in the limelight at the moment but regarded as very promising, such as our theme. Topological disorder refers to the dis order in the positions and connectivities of atoms in amorphous solids and liquids. The development of the physiCS of topologically disorderd systems, though extremely important fundamentally and for application purposes, falls far behind compared to that of other kinds of disorderd systems because the structure characterization of topologically disordered systems is still at a rather primitive stage. The structure characterization is the key to com prehensive understanding of physical properties of any material. Recently, several new attempts at structural analyses have been reported. Encouraged by this fact, our motivation in organizing the symposium was to investigate the possibilities of theoretical approaches to open a breakthrough in the present research situation on this subject. A rough sketch of the problem is made in the Introduction to give the readers a general outline of the subject. Part I is devoted to several at tempts to synthesize and characterize topological disorder more or less by analytical means.

Condensed Matter Field Theory

Alexander Altland,Ben D. Simons
Condensed Matter Field Theory Book PDF

Author : Alexander Altland,Ben D. Simons
Publisher : Cambridge University Press
Page : 785 pages
File Size : 48,8 Mb
Release : 2010-03-11
Category : Science
ISBN : 9780521769754

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Condensed Matter Field Theory by Alexander Altland,Ben D. Simons Pdf

This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.

Modern Condensed Matter Physics

Steven M. Girvin,Kun Yang
Modern Condensed Matter Physics Book PDF

Author : Steven M. Girvin,Kun Yang
Publisher : Cambridge University Press
Page : 720 pages
File Size : 41,5 Mb
Release : 2019-02-28
Category : Science
ISBN : 9781107137394

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Modern Condensed Matter Physics by Steven M. Girvin,Kun Yang Pdf

Comprehensive and accessible coverage from the basics to advanced topics in modern quantum condensed matter physics.

Field Theories of Condensed Matter Physics

Eduardo Fradkin
Field Theories of Condensed Matter Physics Book PDF

Author : Eduardo Fradkin
Publisher : Cambridge University Press
Page : 855 pages
File Size : 50,8 Mb
Release : 2013-02-28
Category : Science
ISBN : 9780521764445

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Field Theories of Condensed Matter Physics by Eduardo Fradkin Pdf

Presenting the physics of the most challenging problems in condensed matter using the conceptual framework of quantum field theory, this book is of great interest to physicists in condensed matter and high energy and string theorists, as well as mathematicians. Revised and updated, this second edition features new chapters on the renormalization group, the Luttinger liquid, gauge theory, topological fluids, topological insulators and quantum entanglement. The book begins with the basic concepts and tools, developing them gradually to bring readers to the issues currently faced at the frontiers of research, such as topological phases of matter, quantum and classical critical phenomena, quantum Hall effects and superconductors. Other topics covered include one-dimensional strongly correlated systems, quantum ordered and disordered phases, topological structures in condensed matter and in field theory and fractional statistics.