Infinite density matrix renormalization group for multicomponent quantum Hall systems

TL;DR

This paper extends the infinite density matrix renormalization group method to multicomponent quantum Hall systems, enabling the study of larger systems and complex interactions, with a focus on the $ u=5/2$ state and Landau level mixing.

Contribution

It develops methodological extensions of iDMRG for multicomponent quantum Hall systems with long-range interactions, allowing analysis of larger systems and complex phases.

Findings

Anti-Pfaffian state is favored over Pfaffian at the Coulomb point.

Methodology enables studying Landau level mixing effects.

Extended accessible system sizes for quantum Hall simulations.

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.