Adiabatic Construction of Hierarchical Quantum Hall States

Abstract

We propose an exact model of anyon ground states including higher Landau levels, and use it to obtain fractionally quantized Hall states at filling fractions $\nu =p/(p(m-1)+1)$ with $m$ odd, from integer Hall states at $\nu =p$ through adiabatic localization of magnetic flux. For appropriately chosen two-body potential interactions, the energy gap remains intact during the process. The construction hence establishes the existence of incompressible states at these fillings.

12pages

References in corpus (6)

• Fractional statistics in anyon collisions
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Prediction of a non-Abelian fractional quantum Hall state with $f$-wave pairing of composite fermions in wide quantum wells
• Energetics of Pfaffian-AntiPfaffian Domains
• Composite anyons on a torus

Cited by in corpus (6)

• Composite anyons on a torus
• Entanglement Action for the Real-Space Entanglement Spectra of Composite Fermion Wave Functions
• Bulk-edge Correspondence in the Adiabatic Heuristic Principle
• Inner workings of fractional quantum Hall parent Hamiltonians: A matrix product state point of view
• Adiabatic Continuity of the Spinful Quantum Hall States
• Crossover from Integer to Fractional Quantum Hall Effect