Construction and Solutions of Quadratic Effective Hamiltonians for Magnetic Impurities

We demonstrate that the chiral symmytry breaking quadratic effective Hamiltonians for magnetic impurities embbeded in a non-interacting fermionic reservoir can be constructued in a self-consistent manner. The solutions of the quadratic effective Hamiltnian corresponds to the ground state and single fermion excitations. Results for Anderson Impurity model and more realistic magnetic inpurities are presented.