Collective edge modes in fractional quantum Hall systems

Over the past few years one of us (Murthy) in collaboration with Shankar has developed an extended Hamiltonian formalism capable of describing the ground-state and low-energy excitations in the fractional quantum Hall regime. The Hamiltonian, expressed in terms of composite fermion operators, incorporates all the nonperturbative features of the fractional Hall regime, so that conventional many-body approximations such as Hartree-Fock and time-dependent Hartree-Fock are applicable. We apply this formalism to develop a microscopic theory of the collective edge modes in fractional quantum Hall regime. We present the results for edge mode dispersions at principal filling factors $\ensuremath{\nu}=1∕3$, $1∕5$, and $2∕5$ for systems with unreconstructed edges. The primary advantage of the method is that one works in the thermodynamic limit right from the beginning, thus avoiding the finite-size effects which ultimately limit exact diagonalization studies.