Infinite density matrix renormalization group for multicomponent quantum Hall systems

Abstract

While the simplest quantum Hall plateaus, such as the $\nu =1/3$ 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 $\nu =5/2$, 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 $\nu =5/2$ 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.

12 pages, 9 figures. v2 added more data for different amounts of Landau level mixing at 5/2 filling

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