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While the simplest quantum Hall plateaus, such as the $\nu = 1/3$ state inGaAs, can be conveniently analyzed by assuming only a single active Landaulevel participates, for many phases the spin, valley, bilayer, subband, orhigher Landau level indices play an important role. These `multi-component'problems are difficult to study using exact diagonalization because eachcomponent increases the difficulty exponentially. An important example is theplateau at $\nu = 5/2$, where scattering into higher Landau levels choosesbetween the competing non-Abelian Pfaffian and anti-Pfaffian states. We addressthe methodological issues required to apply the infinite density matrixrenormalization group to quantum Hall systems with multiple components andlong-range Coulomb interactions, greatly extending accessible system sizes. Asan initial application we study the problem of Landau level mixing in the $\nu= 5/2$ state. Within the approach to Landau level mixing used here, we findthat at the Coulomb point the anti-Pfaffian is preferred over the Pfaffianstate over a range of Landau level mixing up to the experimentally relevantvalues.

Infinite density matrix renormalization group for multicomponent quantum Hall systems