Effective field theory for the bulk and edge states of quantum Hall states in unpolarized single layer and bilayer systems

Abstract

We present an effective theory for the bulk Fractional Quantum Hall states in spin-polarized bilayer and spin-1/2 single layer two-dimensional electron gases (2DEG) in high magnetic fields consistent with the requirement of global gauge invariance on systems with periodic boundary conditions. We derive the theory for the edge states that follows naturally from this bulk theory. We find that the minimal effective theory contains two propagating edge modes that carry charge and energy, and two non-propagating topological modes responsible for the statistics of the excitations. We give a detailed description of the effective theory for the spin-singlet states, the symmetric bilayer states and for the $(m,m,m)$ states. We calculate explicitly, for a number of cases of interest, the operators that create the elementary excitations, their bound states, and the electron. We also discuss the scaling behavior of the tunneling conductances in different situations: internal tunneling, tunneling between identical edges and tunneling into a FQH state from a Fermi liquid.

27 pages; new subsection with summary of results and two tables. Misprints and errors of an an earlier version are corrected. In particular the tunneling exponents for the SU(2) states at 2/3 and 4/7 have been corrected; same with the electron operator for the 2/3 state

References in corpus (2)

• Evidence for a Goldstone Mode in a Double Layer Quantum Hall System
• Non-equilibrium tunneling into general quantum Hall edge states

Cited by in corpus (17)

• Topological Entanglement Entropy in Chern-Simons Theories and Quantum Hall Fluids
• Charge tunneling in fractional edge channels
• Separation of spin and charge in paired spin-singlet quantum Hall states
• Fermion Chern Simons Theory of Hierarchical Fractional Quantum Hall States
• Landau-Level Mixing and Particle-Hole Symmetry Breaking for Spin Transitions in the Fractional Quantum Hall Effect
• Inter edge Tunneling in Quantum Hall Line Junctions
• Microscopic Study of Edge Excitations of Spin-Polarized and Spin-Unpolarized $\nu =2/3$ Fractional Quantum Hall Effect
• SU(N) fractional quantum Hall effects in topological flat bands
• Cooper pair tunneling in junctions of singlet quantum Hall states and superconductors
• Mutual Composite Fermion and composite Boson approaches to balanced and imbalanced bilayer quantum Hall system: an electronic analogy of the Helium 4 system
• Quantum phase transition in a multicomponent anyonic Lieb-Liniger model
• Parafermions, induced edge states and domain walls in the fractional quantum Hall effect spin transitions
• Topological characterization of hierarchical fractional quantum Hall effects in topological flat bands with SU($N$) symmetry
• On ground states of interacting Composite Fermions with spin at half filling
• Fractional statistics and duality: strong tunneling behavior of edge states of quantum Hall liquids in the Jain sequence
• Infrared catastrophe and tunneling into strongly correlated electron systems: Perturbative x-ray edge limit
• Infrared catastrophe and tunneling into strongly correlated electron systems: Exact solution of the x-ray edge limit for the 1D electron gas and 2D Hall fluid