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An Anyon Primer

Sumathi Rao

Published Sep 18, 1992• 15 citations
OpenAlex

Abstract

In this set of lectures, we give a pedagogical introduction to the subject of anyons. We discuss 1) basic concepts in anyon physics, 2) quantum mechanics of two anyon systems, 3) statistical mechanics of many anyon systems, 4) mean field approach to many anyon systems and anyon superconductivity, 5) anyons in field theory and 6) anyons in the Fractional Quantum Hall Effect (FQHE). (Based on lectures delivered at the VII SERC school in High Energy Physics at the Physical Research Laboratory, Ahmedabad, January 1992 and at the I SERC school in Statistical Mechanics at Puri, February 1994.)

Related papers

An Anyon Primer

Sumathi Rao

In this set of lectures, we give a pedagogical introduction to the subject of anyons. We discuss 1) basic concepts in anyon physics, 2) quantum mechanics of two anyon systems, 3) statistical mechanics of many anyon systems, 4) mean field approach to many anyon systems and anyon superconductivity, 5) anyons in field theory and 6) anyons in the Fractional Quantum Hall Effect (FQHE). (Based on lectures delivered at the VII SERC school in High Energy Physics at the Physical Research Laboratory, Ahmedabad, January 1992 and at the I SERC school in Statistical Mechanics at Puri, February 1994.)

arXiv:hep-th/9209066•Sep 18, 1992•1 citation

Anyons

I. J. R. Aitchison, Nick E. Mavromatos

An elementary introduction is given to the concept of anyons—quantum particles whose ‘statistics’ interpolate smoothly between those of bosons and fermions. Such particles—or quasi-particle excitations—can occur in two-dimensional systems in which the particles experience strong short-range mutual repulsions. These circumstances effectively mean that one has to apply quantum mechanics to a configuration space in which some points are excluded (i.e. it has ‘holes’)—namely, those points where two particles would coincide. The Aharonov—Bohm effect provides the simplest physical example of quantum mechanics in such a non-simply connected space, and is also fundamental to a simple model for anyons. A qualitative introduction is given to two currently proposed physical applications of anyons: high temperature superconductivity, and the (fractional) quantum Hall effect.

Contemporary Physics•Jul 1, 1991•28 citations

Quantum Hall systems

Lucjan Jacak, Piotr Sitko, Konrad Wieczorek +1 more

Abstract The book presents the wide range of topics in two-dimensional physics of quantum Hall systems, especially fractional quantum Hall states. It starts with the fundamental problems of quantum statistics in two dimensions and the corresponding braid group formalism. The braid group formalism of anyons (previously known) is developed for composite fermions. The effective formalism used in many-body quantum Hall theories — the Chern–Simons theory is also presented. The Chern–Simons theory of anyons (particles obeying fractional statistics) and composite fermions (related to Hall systems) is given, in detail. Numerical studies, which play the important role in quantum Hall analyses, are presented for spherical systems (Haldane sphere). The composite fermion theory is tested in numerical studies. The concept of the hierarchy of condensed states of composite fermion excitations is introduced (in analogy to the Haldane hierarchy). The hierarchies of odd-denominator states and even-denominator states are presented. The BCS paired Hall state is also discussed. An introduction to multi-component quantum Hall systems and spin quantum Hall systems is sketched.

Oxford University Press eBooks•Sep 25, 2003•17 citations

Fractional Statistics and Quantum Theory

Avinash Khare

This book explains the subtleties of quantum statistical mechanics in lower dimensions and their possible ramifications in quantum theory. The discussion is at a pedagogical level and is addressed to both graduate students and advanced research workers with a reasonable background in quantum and statistical mechanics. The main emphasis will be on explaining new concepts. Topics in the first part of the book includes the flux tube model of anyons, the braid group and quantum and statistical mechanics of noninteracting anyon gas. The second part of the book provides a detailed discussion about f

WORLD SCIENTIFIC eBooks•Mar 1, 1998•140 citations

Low-dimensional quantum field theories for condensed matter physicists : lecture notes of ICTP Summer Course, Trieste, Italy, September 1992

Stig Lundqvist, G. Morandi, Lu Yu

Some geometry and toplogy, G. Marmo and G. Morandi gauge symmetries, toplogy and quantisation, A.P. Balachandran the Chern-Simons-Landau-Ginzburg theory of the fractional quantum Hall effect, S.C. Zhang universitality in the fractional quantum hall, E. Fradkin and A. Lopez anyons and anyon superconductivity, A.L. Fetter bosonization - how to make it work for you in condensed matter, R. Shankar methods of conformal field theory in condensed matter physics, A.W.W. Ludwig integrable models in condensed matter physics, N. Andrei quantum antiferromagnets in two dimensions, S. Sachdev.

WORLD SCIENTIFIC eBooks•Jan 1, 1995•18 citations

Introduction to superfluidity -- Field-theoretical approach and applications

Andreas Schmitt

In this pedagogical introduction, I discuss theoretical aspects of superfluidity and superconductivity, mostly using a field-theoretical formalism. While the emphasis is on general concepts and mechanisms behind superfluidity, I also discuss various applications in low-energy and high-energy physics. Besides some introductory and standard topics such as superfluid helium and superfluidity in a simple scalar field theory, the lecture notes also include more advanced chapters, for instance discussions of the covariant two-fluid formalism and Cooper pairing with mismatched Fermi surfaces.

arXiv:1404.1284•Apr 4, 2014•27 citations
In this set of lectures, we give a pedagogical introduction to the subject of anyons. We discuss 1) basic concepts in anyon physics, 2) quantum mechanics of two anyon systems, 3) statistical mechanics of many anyon systems, 4) mean field approach to many anyon systems and anyon superconductivity, 5) anyons in field theory and 6) anyons in the Fractional Quantum Hall Effect (FQHE). (Based on lectures delivered at the VII SERC school in High Energy Physics at the Physical Research Laboratory, Ahmedabad, January 1992 and at the I SERC school in Statistical Mechanics at Puri, February 1994.)
In this set of lectures, we give a pedagogical introduction to the subject of anyons. We discuss 1) basic concepts in anyon physics, 2) quantum mechanics of two anyon systems, 3) statistical mechanics of many anyon systems, 4) mean field approach to many anyon systems and anyon superconductivity, 5) anyons in field theory and 6) anyons in the Fractional Quantum Hall Effect (FQHE). (Based on lectures delivered at the VII SERC school in High Energy Physics at the Physical Research Laboratory, Ahmedabad, January 1992 and at the I SERC school in Statistical Mechanics at Puri, February 1994.)
An elementary introduction is given to the concept of anyons—quantum particles whose ‘statistics’ interpolate smoothly between those of bosons and fermions. Such particles—or quasi-particle excitations—can occur in two-dimensional systems in which the particles experience strong short-range mutual repulsions. These circumstances effectively mean that one has to apply quantum mechanics to a configuration space in which some points are excluded (i.e. it has ‘holes’)—namely, those points where two particles would coincide. The Aharonov—Bohm effect provides the simplest physical example of quantum mechanics in such a non-simply connected space, and is also fundamental to a simple model for anyons. A qualitative introduction is given to two currently proposed physical applications of anyons: high temperature superconductivity, and the (fractional) quantum Hall effect.
Abstract The book presents the wide range of topics in two-dimensional physics of quantum Hall systems, especially fractional quantum Hall states. It starts with the fundamental problems of quantum statistics in two dimensions and the corresponding braid group formalism. The braid group formalism of anyons (previously known) is developed for composite fermions. The effective formalism used in many-body quantum Hall theories — the Chern–Simons theory is also presented. The Chern–Simons theory of anyons (particles obeying fractional statistics) and composite fermions (related to Hall systems) is given, in detail. Numerical studies, which play the important role in quantum Hall analyses, are presented for spherical systems (Haldane sphere). The composite fermion theory is tested in numerical studies. The concept of the hierarchy of condensed states of composite fermion excitations is introduced (in analogy to the Haldane hierarchy). The hierarchies of odd-denominator states and even-denominator states are presented. The BCS paired Hall state is also discussed. An introduction to multi-component quantum Hall systems and spin quantum Hall systems is sketched.
This book explains the subtleties of quantum statistical mechanics in lower dimensions and their possible ramifications in quantum theory. The discussion is at a pedagogical level and is addressed to both graduate students and advanced research workers with a reasonable background in quantum and statistical mechanics. The main emphasis will be on explaining new concepts. Topics in the first part of the book includes the flux tube model of anyons, the braid group and quantum and statistical mechanics of noninteracting anyon gas. The second part of the book provides a detailed discussion about f
Some geometry and toplogy, G. Marmo and G. Morandi gauge symmetries, toplogy and quantisation, A.P. Balachandran the Chern-Simons-Landau-Ginzburg theory of the fractional quantum Hall effect, S.C. Zhang universitality in the fractional quantum hall, E. Fradkin and A. Lopez anyons and anyon superconductivity, A.L. Fetter bosonization - how to make it work for you in condensed matter, R. Shankar methods of conformal field theory in condensed matter physics, A.W.W. Ludwig integrable models in condensed matter physics, N. Andrei quantum antiferromagnets in two dimensions, S. Sachdev.
In this pedagogical introduction, I discuss theoretical aspects of superfluidity and superconductivity, mostly using a field-theoretical formalism. While the emphasis is on general concepts and mechanisms behind superfluidity, I also discuss various applications in low-energy and high-energy physics. Besides some introductory and standard topics such as superfluid helium and superfluidity in a simple scalar field theory, the lecture notes also include more advanced chapters, for instance discussions of the covariant two-fluid formalism and Cooper pairing with mismatched Fermi surfaces.