Adiabatic Construction of Hierarchical Quantum Hall States

TL;DR

This paper introduces an exact model for anyon ground states across Landau levels, demonstrating the adiabatic transition from integer to fractional quantum Hall states with preserved energy gaps, confirming incompressibility at specific fillings.

Contribution

It presents a novel exact model for constructing hierarchical quantum Hall states including higher Landau levels, using adiabatic flux localization to connect integer and fractional states.

Findings

Fractionally quantized Hall states at specific filling fractions.

Energy gap remains stable during adiabatic process.

Establishes the existence of incompressible states at these fillings.

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.