Exact isolated and isothermal susceptibilities for an interacting dipole-lattice system

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Abstract
Relationships between the static isothermal susceptibility and the dynamic susceptibility as given by linear-response theory (isolated susceptibility) are investigated by means of an exactly soluble model of a two-level dipole moment interacting with phonons. Two forms of dipole-lattice interaction coupling are treated: coupling to lattice strain and coupling to lattice atomic displacements (piezoelectric coupling). In the case of piezoelectric coupling and for the temperature limits investigated, the isolated susceptibility follows closely the behavior predicted by a simple Debye theory with a one-phonon relaxation time predicted by the model. There are deviations from this behavior when the dipole-lattice coupling becomes strong. Static isolated susceptibilities for various cases are compared with the corresponding static isothermal susceptibilities. Two cases in which these two static susceptibilities differ are discussed: the case of strain coupling and that of piezoelectric coupling with a lower-frequency cutoff in the phonon spectrum which couples to the dipole. The occurrence of this difference is related to the nonergodic behavior of the polarization autocorrelation function which is in turn influenced by the existence of degeneracies in the model. It is further demonstrated that the addition of a symmetry-breaking term will remove the discrepancy between the two static susceptibilities at the expense, however, of creating a singularity in the dynamic isolated susceptibility associated with a low-lying zero-phonon absorption.