Dynamical Effective Medium Theory for Quantum Spins and Multipoles

Abstract

A dynamical effective medium theory is presented for quantum spins andhigher multipoles such as quadrupole moments.The theory is a generalization of the spherical model approximationfor the Ising model, and is accurate up to O(1/z_n) where z_n isthe number of interacting neighbors.The polarization function is optimized under the condition that it bediagonal in site indices. With use of auxiliary fields and path integrals, the theory isflexibly applied to quantum spins and higher multipoles with manyinteracting neighbors.A Kondo-type screening of each spin is proposed for systems withextreme quantum fluctuations but without conduction electrons.