We study the effects of anisotropic interactions in the quantum Hall effect in the presence of a fourfold discrete rotational symmetry. Employing the density matrix renormalization group technique on an infinite cylinder geometry (iDMRG), we calculate the anisotropy response of the Laughlin state at and the composite-Fermi liquid (CFL) state at . We find that the anisotropy transferred from the interaction potential to the state is stronger when compared with the complementary case of an anisotropic band. Further, the strength of anisotropy reduces as the interaction is made shorter ranged. Quite surprisingly, at , the deformation in the CF Fermi surface changes sign as the interaction range is reduced. Our results imply that the short-distance and long-distance parts of the interaction potential have opposite effects on the CFL state in the presence of -symmetric anisotropy.
All Science Journal Classification (ASJC) codes
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics