University of Kentucky

Title: Dots hit the fan: exact solution of disordered interacting quantum dots

Abstract: Understanding the combined effects of disorder and interactions in electronic systems has emerged as one of the most challenging theoretical problems in condensed matter physics. It turns out that one can completely solve this problem in a particular regime, when the system is finite (as in a quantum dot) but its dimensionless conductance g under open-lead conditions is large. This regime is experimentally interesting for the statistics of Coulomb Blockade in quantum dots. First some RG work will be described which shows that a disordered quantum dot with Fermi liquid interactions can be in one of two phases; one controlled by a constant exchange and interaction model (a.k.a the "Universal Hamiltonian") and another regime where fluctuations become large. These two are separated in the infinite-g limit by a second-order phase transition. Next we solve the strong-coupling phase, which is characterized by a Fermi surface distortion, by a large-N approximation (where N=g is in fact large for realistic systems). Predictions will be presented for finite but large g for the statistics of the Coulomb Blockade peak spacings and other correlators. A connection will also be made to ideas concerning "Fock space localization".