Geometry of flux attachment in anisotropic fractional quantum Hall states

Abstract

Fractional quantum Hall (FQH) states are known to possess an internal metric degree of freedom that allows them to minimize their energy when contrasting geometries are present in the problem (e.g., electron band mass and dielectric tensor). We investigate the internal metric of several incompressible FQH states by probing its response to band mass anisotropy using infinite DMRG simulations on a cylinder geometry. We test and apply a method to extract the internal metric of a FQH state from its guiding center structure factor. We find that the response to band mass anisotropy is approximately the same for states in the same Jain sequence, but changes substantially between different sequences. We provide a theoretical explanation of the observed behavior of primary states at filling $\nu =1/m$ in terms of a minimal microscopic model of flux attachment.

12 pages including references, 14 figures

References in corpus (10)

• Infinite density matrix renormalization group for multicomponent quantum Hall systems
• Band mass anisotropy and the intrinsic metric of fractional quantum Hall systems
• Topological central charge from Berry curvature: gravitational anomalies in trial wavefunctions for topological phases
• Theory of Nematic Fractional Quantum Hall State
• Transference of Transport Anisotropy to Composite Fermions
• Fractional quantum Hall states in two-dimensional electron systems with anisotropic interactions
• Fractional quantum Hall systems near nematicity: bimetric theory, composite fermions, and Dirac brackets
• Composite Fermions with a Warped Fermi Contour
• Anisotropic Pseudopotential Characterization of Quantum Hall Systems under Tilted Magnetic Field
• Composite fermions in bands with N-fold rotational symmetry

Cited by in corpus (7)

• Giant spontaneous Hall effect in a nonmagnetic Weyl-Kondo semimetal
• Theory of fractional quantum Hall liquids coupled to quantum light and emergent graviton-polaritons
• Interaction-dependent anisotropy of fractional quantum Hall states
• Charge density waves and their transitions in anisotropic quantum Hall systems
• Anisotropy and quench dynamics of quasiholes in fractional quantum Hall liquids
• Chiral Gravitons on the Lattice
• Chiral Graviton Modes in Fermionic Fractional Chern Insulators