Hamiltonian theory of gaps, masses and polarization in quantum Hall states: full disclosure

Abstract

I furnish details of the hamiltonian theory of the FQHE developed with Murthy for the infrared, which I subsequently extended to all distances and apply it to Jain fractions ν= p/(2ps + 1). The explicit operator description in terms of the CF allows one to answer quantitative and qualitative issues, some of which cannot even be posed otherwise. I compute activation gaps for several potentials, exhibit their particle hole symmetry, the profiles of charge density in states with a quasiparticles or hole, (all in closed form) and compare to results from trial wavefunctions and exact diagonalization. The Hartree-Fock approximation is used since much of the nonperturbative physics is built in at tree level. I compare the gaps to experiment and comment on the rough equality of normalized masses near half and quarter filling. I compute the critical fields at which the Hall system will jump from one quantized value of polarization to another, and the polarization and relaxation rates for half filling as a function of temperature and propose a Korringa like law. After providing some plausibility arguments, I explore the possibility of describing several magnetic phenomena in dirty systems with an effective potential, by extracting a free parameter describing the potential from one data point and then using it to predict all the others from that sample. This works to the accuracy typical of this theory (10 -20 percent). I explain why the CF behaves like free particle in some magnetic experiments when it is not, what exactly the CF is made of, what one means by its dipole moment, and how the comparison of theory to experiment must be modified to fit the peculiarities of the quantized Hall problem.