On the implications of discrete symmetries for the β-function of quantum Hall systems Academic Article uri icon

  •  
  • Overview
  •  
  • Research
  •  
  • Identity
  •  
  • Additional Document Info
  •  
  • View All
  •  

abstract

  • We argue that the large discrete symmetry group of quantum Hall systems is insufficient in itself to determine the complete beta function for the scaling of the conductivities, $\sigma_{xx}$ and $\sigma_{xy}$. We illustrate this point by showing that a recent ansatz for this function is one of a many-parameter family. A clean prediction for the delocalization exponents for these systems therefore requires the specification of more information, such as past proposals that the beta function is either holomorphic or quasi-holomorphic in the variable $z = (\hbar/e^2)(\sigma_{xy} + i\sigma_{xx})$.

publication date

  • April 1999