Ground-State Magnetization for Interacting Fermions in a Disordered Potential : Kinetic Energy, Exchange Interaction and Off-Diagonal Fluctuations

Philippe Jacquod, A. Douglas Stone

Published 2001-02-06, updated 2001-10-05Version 2

We study a model of interacting fermions in a disordered potential, which is assumed to generate uniformly fluctuating interaction matrix elements. We show that the ground state magnetization is systematically decreased by off-diagonal fluctuations of the interaction matrix elements. This effect is neglected in the Stoner picture of itinerant ferromagnetism in which the ground-state magnetization is simply determined by the balance between ferromagnetic exchange and kinetic energy, and increasing the interaction strength always favors ferromagnetism. The physical origin of the demagnetizing effect of interaction fluctuations is the larger number of final states available for interaction-induced scattering in the lower spin sectors of the Hilbert space. We analyze the energetic role played by these fluctuations in the limits of small and large interaction $U$. In the small $U$ limit we do second-order perturbation theory and identify explicitly transitions which are allowed for minimal spin and forbidden for higher spin. These transitions then on average lower the energy of the minimal spin ground state with respect to higher spin. For large interactions $U$ we amplify on our earlier work [Ph. Jacquod and A.D. Stone, Phys. Rev. Lett. 84, 3938 (2000)] which showed that minimal spin is favored due to a larger broadening of the many-body density of states in the low-spin sectors. Numerical results are presented in both limits.