A Compact Approximate Solution to the Kondo Problem

A compact approximate groundstate of the Kondo problem is introduced. It consists of four Slater states. The spin up and down states of the localized d-impurity are paired with two localized selectron states of opposite spin. All the remaining s-electron states are rearranged forming two new optimal orthonormal bases. Through a rotation in Hilbert space the two localized states (and the rest of the bases) are optimized by minimizing the energy expectation value. The ground-state energ y E00 and the singlet-triplet excitation energy ∆Est are calculated numerically. Although the two energies can differ by a factor of 1000, they are obtained simultaneously. The singlet-triplet excitation energy ∆Est is proportional to exp [−1/2Jρ] and quite close to the Kondo temperature kBTK . The cases for antiferromagnetic (J > 0) and ferromagnetic (J < 0) coupling are investigated. PACS: 75.20.Hr, 72.15.Rn