Quantum Hall Effects: Field Theoretical Approach and Related Topics

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 ChernSimons 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.

Contents:

• Quantum Field Theory:
• Quantum Mechanics
• Quantum Field Theory
• Canonical Quantization
• Spontaneous Symmetry Breaking
• Electromagnetic Field
• Topological Solitons
• Anyons
• Monolayer Quantum Hall Systems:
• Landau Quantization
• Quantum Hall Effects
• Quasiparticles and Activation Energy
• Field Theory of Composite Particles
• Composite Bosons and Semiclassical Analysis
• Quantum Hall Ferromagnets
• Spin Textures
• Hierarchy of Fractional Quantum Hall States
• Edge Effects
• Bilayer Quantum Hall Systems:
• SU(2) Pseudospin Structure
• Bilayer-Locked States
• Interlayer-Coherent States
• Skyrmions in SU(4)-Invariant Regime
• Bilayer Quantum-Hall Junction
• Algebraic Approach:
• Lowest-Landau-Level Projection
• Quantum Hall Effects in Algebraic Approach
• Effective Hamiltonian in Algebraic Approach
• Electric Currents in Bilayer Systems