Exact solution for spin and charge correlations in quantum dots: Effect of level fluctuations and Zeeman splitting

The inclusion of charging and spin-exchange interactions within the universal Hamiltonian description of quantum dots is challenging as it leads to a non-Abelian action. Here we present an exact analytical solution to the problem, in particular, in the vicinity of the Stoner instability. We calculate the tunneling density of states and the spin susceptibility. We demonstrate that near the Stoner instability the spin susceptibility follows a Curie law with an effective spin. The latter depends logarithmically on temperature due to the statistical fluctuations of the single-particle levels. Near the Stoner instability the tunneling density of states exhibits a nonmonotonous behavior as a function of the tunneling energy, even at temperatures higher than the exchange energy. This is due to enhanced spin correlations. Our results could be tested in quantum dots made of nearly ferromagnetic materials.