Kondo effect and continuous quantum phase transitions in double quantum dots with on-site and interdot repulsion and magnetic field

Abstract

By means of the numerical renormalization group method, I study the Kondo effect and quantum phase transitions in a double quantum dot system with on-site repulsion $U$, interdot repulsion $V,$ and magnetic field $B$. At zero temperature and $B=0$, there is a local spin triplet-singlet transition of the Kosterlitz-Thouless type when $V$ increases to a critical value ${V}_{c}\ensuremath{\approx}U$. With increasing $B$, a singlet-triplet transition of the second order occurs at a critical magnetic field ${B}_{c}\ensuremath{\approx}V\ensuremath{-}U$. The magnetic susceptibility and the first derivatives of the spin correlation and double occupation are expected to diverge at ${B}_{c}$ and to have different critical exponents, which are universal for different parameters. An appropriate magnetic field can restore the Kondo effect.