While the simplest quantum Hall plateaus, such as the ν=1/3 state in
GaAs, can be conveniently analyzed by assuming only a single active Landau
level participates, for many phases the spin, valley, bilayer, subband, or
higher Landau level indices play an important role. These `multi-component'
problems are difficult to study using exact diagonalization because each
component increases the difficulty exponentially. An important example is the
plateau at ν=5/2, where scattering into higher Landau levels chooses
between the competing non-Abelian Pfaffian and anti-Pfaffian states. We address
the methodological issues required to apply the infinite density matrix
renormalization group to quantum Hall systems with multiple components and
long-range Coulomb interactions, greatly extending accessible system sizes. As
an initial application we study the problem of Landau level mixing in the ν=5/2 state. Within the approach to Landau level mixing used here, we find
that at the Coulomb point the anti-Pfaffian is preferred over the Pfaffian
state over a range of Landau level mixing up to the experimentally relevant
values.Comment: 12 pages, 9 figures. v2 added more data for different amounts of
Landau level mixing at 5/2 fillin
