Dynamical Effective Medium Theory for Quantum Spins and Multipoles

TL;DR

This paper develops a dynamical effective medium theory for quantum spins and multipoles, generalizing the spherical model approximation to handle complex interactions and quantum fluctuations.

Contribution

It introduces a flexible, optimized approach using auxiliary fields and path integrals for quantum spins and multipoles, extending the spherical model approximation.

Findings

Accurate up to O(1/z_n) for large neighbor interactions

Proposes a Kondo-type screening mechanism for quantum fluctuations

Applicable to systems without conduction electrons

Abstract

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