The coherent potential approximation
Series in condensed matter physics · 2008
A family of random models for bosonic quasi-particle excitations, e.g. the vibrations of a disordered solid, is introduced.The generator of the linearized phase space dynamics of these models is the sum of a deterministic and a random part.The former may describe any model of N identical phonon bands, while the latter is a d-dimensional generalization of the random matrix model of Lueck, Sommers, and Zirnbauer (LSZ).The models are constructed so as to exclude the unphysical occurrence of runaway solutions.By using the Efetov-Wegner supersymmetry method in combination with the new technique of superbosonization, the disordered boson model is cast in the form of a supermatrix field theory.A self-consistent approximation of mean-field type arises from treating the field theory as a variational problem.The resulting scheme, referred to as a coherent potential approximation, becomes exact for large values of N. In the randommatrix limit, agreement with the results of LSZ is found.The self-consistency equation for the full d-dimensional problem is solved numerically.