Quantum Hall Effects Field Theoretical Approach and Related Topics 1st Edition by Zyun Francis Ezawa 9789810234300 9810234309

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ISBN 10: 9810234309
ISBN 13: 9789810234300
Author: Zyun Francis Ezawa

Tremendous theoretical and experimental developments have recently been made in the sphere of the quantum Hall effect. Among them a field-theoretical approach has presented a fascinating unified physical picture. A most significant feature of the quantum Hall system is that exotic phenomena associated with statistics transmutation are realized. For instance, an electron may undergo Bose condensation by making a charge-flux composite, and fractionally charged excitations (anyons) emerge as quasiparticles. A pedagogical and self-contained discussion on monolayer and bilayer quantum Hall systems is given in a field-theoretical framework, together with an introduction to quantum field theory, anyon physics and Chern-Simons gauge theory. Only knowledge of quantum mechanics is assumed.This invaluable book will be of great interest to students and researchers in condensed-matter, theoretical, particle and mathematical physics.

Quantum Hall Effects Field Theoretical Approach and Related Topics 1st Table of contents:

Part I – Quantum Field Theory

1. Quantum Mechanics

• Hilbert Spaces

• Hamiltonian Formalism

• Creation and Annihilation Operators

• Uncertainty Principle

• Coherent States and Squeezed States

• Particle Number and Phase

• Macroscopic Coherence

2. Quantum Field Theory

• One-Body Hamiltonian

• Many-Body Hamiltonian

• Boson Field Operators

• Quantum Field Theory

• Fermion Field Operators

3. Canonical Quantization

• Relativistic Particles and Waves

• Schrödinger Field

• Real Klein-Gordon Field

• Complex Klein-Gordon Field

• Noether Currents

4. Spontaneous Symmetry Breaking

• Ferromagnets

• Real Klein-Gordon Field

• Complex Klein-Gordon Field

• Sigma Model

• Schrödinger Field

• Superfluidity

• Goldstone Theorem

5. Electromagnetic Field

• Maxwell Equations

• Canonical Quantization

• Interaction with Matter Field

• Anderson-Higgs Mechanism

• Massive Vector Field

• Superconductivity

6. Topological Solitons

• Topological Sectors

• Classical Fields

• Solitary Waves, Kinks, and Solitons

• Sine-Gordon Solitons

• Vortex Solitons

• Homotopy Classes

• Skyrmions in Planar Geometry

• CPN-1 Skyrmions

7. Anyons

• Spin and Statistics

• Fractional Statistics

• Quantum Mechanics

• Aharonov-Bohm Effect

Part II – Monolayer Quantum Hall Systems

8. Introduction

9. Landau Quantization

• Planar Electrons

• Cyclotron Motion

• Hall Current

• Symmetric Gauge

• Landau Gauge

• Lowest-Landau-Level Condition

10. Quantum Hall Effects

• Incompressibility

• Integer Quantum Hall Effects

• Fractional Quantum Hall Effects

• Quasiparticles

• Hall Plateaux

11. Quasiparticles and Activation Energy

• Impurity Potentials

• Gap Energies

• Dispersion Relation

• Thermal Activation

12. Field Theory of Composite Particles

• Composite Particles

• Statistical Transmutation

• Effective Magnetic Field

• Dressed Composite Particles

• Composite Particles in Lowest Landau Level

• Composite Fermions in Lowest Landau Level

13. Composite Bosons and Semiclassical Analysis

• Semiclassical Ground State

• Vortex Excitations

• Field Theory of Vortex Solitons

• Haldane-Halperin Hierarchy

14. Quantum Hall Ferromagnets

• Spin Coherence

• Spin Degree of Freedom

• SU(2) Composite Bosons

• Wave Functions

• Spin Field, Sigma Field, and CP1 Field

• Effective Hamiltonian

15. Spin Textures

• Spin Excitations

• Skyrmions

• Skyrmion Energy

16. Hierarchy of Fractional Quantum Hall States

• Jain Hierarchy

• Landau Levels of Composite Fermions

• Beyond Principal Sequences

• Spin Polarization

• Gap Energies

17. Edge Effects

• Shot Noises of Fractional Charges

• Chiral Edge Excitations

• Chiral Luttinger Liquid

• Electrodynamics on Edge

• Edge Tunneling and Sine-Gordon Solitons

Part III – Bilayer Quantum Hall Systems

18. Introduction

19. SU(2) Pseudospin Structure

• Bilayer Planar Electrons

• Gate Bias Voltages

• Pseudospins

• Compound States

• Charge-Transferable States

• Phase Diagrams

20. Bilayer-Locked States

• Composite-Boson Field

• Wave Functions

• Ground State

• Vortex Excitations

21. Interlayer-Coherent States

• Interlayer Coherence

• Composite Bosons

• CP1 Field

• Ground State

• Goldstone Mode

• Pseudospin Textures

22. Skyrmions in SU(4)-Invariant Regime

• SU(4)-Invariant Regime

• CP3 Skyrmions

• Spin-Skyrmions at v = 1

• Spin-Pseudospin Coherence at v = 2

• Compound State at v = 2

23. Bilayer Quantum-Hall Junction

• Josephson-Like Phenomena

• Parallel Magnetic Field

• Effective Hamiltonian

• Commensurate-Incommensurate Phase Transition

• Josephson Junction vs. Quantum-Hall Junction

• Plasmon Excitations

• Josephson-Like Effects

Part IV – Algebraic Approach

24. Introduction

25. Lowest-Landau-Level Projection

• Quantum Mechanics

• Quantum Field Theory

• Magnetic Translation

• Moyal Algebra

• Edge States

26. Quantum Hall Effects in Algebraic Approach

• Spinless Quantum Hall States

• Hall Current

• Noether Currents

• W∞×SU(2) Density Algebra

• Monolayer Quantum Hall Ferromagnets

• Spin Textures

27. Effective Hamiltonian in Algebraic Approach

• Bilayer Quantum Hall States

• Static Correlation Functions

• Effective Hamiltonian for Coherent Modes

28. Electric Currents in Bilayer Systems

• Electric Currents

• Hall Current

• Screening Current

• Tunneling Current

Appendices

A. Hausdorff Formulas
B. Pauli Matrices
C. Cauchy-Riemann Equations
D. Bogoliubov Transformation
E. Energy-Momentum Tensor
F. Exchange Interaction
G. One-Dimensional Soliton Solutions
H. Field-Theoretical Vortex Operators
I. Perturbative Analysis
J. Bosonization in One-Dimensional Space

References

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