Non-interacting Symmetric Single-Impurity Anderson Model on a Lattice at Finite Temperatures

We study the non-interacting single-impurity Anderson model (resonant level model) on a lattice at finite temperature as an illustrative example for an exactly solvable quantum-mechanical problem, and derive the free energy, various thermodynamic potentials (internal energy, entropy, magnetization), and response functions (specific heat, zero-field magnetic susceptibility). We calculate the magnetic screening cloud, and derive the corresponding correlation length in one dimension beyond which the correlations decay exponentially. The present results remain qualitatively applicable for the interacting single-impurity Anderson model when the energy scale < SIC > CYRILLIC CAPITAL LETTER GHE of the resonant-level model is replaced by the Kondo scale T-K.