The effect of disorder on symmetry breaking in quantum Hall systems

We have been investigating quantum Hall systems by direct diagonalization and the density matrix renormalization group (DMRG). Calculations of the projected density-density correlation function for 10 electrons in 20 orbitals and 12 electrons in 24 orbitals indicate that disorder makes the correlation function behave more regularly with respect to system size. For these system sizes, randomness tends to enhance symmetry breaking when the wavelength of an additional imposed periodic potential is less than the wavelength of the stripe ordering. To investigate larger system sizes, preliminary calculations have been done using DMRG with momentum conservation in the y-direction. With our implementation of DMRG, promising results were obtained for the N = 0 Landau level. It seems more difficult to obtain reliable results in the N = 2 Landau level.