Spin in a Fluctuating Field: The Bose (+Fermi) Kondo models

TL;DR

This paper explores impurity spin models coupled to fluctuating Gaussian fields, revealing controlled fixed points, power-law decay of spin correlations, and phase transitions influenced by Kondo coupling, relevant for magnetic transitions and Kondo lattice systems.

Contribution

It introduces models with impurity spins coupled to fluctuating fields, analyzing their fixed points, correlation decay, and phase transitions, extending understanding of impurity behavior near magnetic quantum critical points.

Findings

Controlled fixed points for models with Gaussian field fluctuations.

Power-law decay of spin correlations for positive epsilon.

Phase transition from Kondo to fluctuation-dominated phase with Kondo coupling.

Abstract

I consider models with an impurity spin coupled to a fluctuating gaussian field with or without additional Kondo coupling of the conventional sort. In the case of isotropic fluctuations, the renormalisation group flows for these models have controlled fixed points when the autocorrelation of the gaussian field $h(t)$, $<T h(t) h(0)> \sim {1\over t^{2-\epsilon}}$ with small positive $\epsilon$. In absence of any additional Kondo coupling, I get powerlaw decay of spin correlators, $<T S(t) S(0)> \sim {1\over t^{\epsilon}}$ . For negative $\epsilon$, the spin autocorrelation is constant in long time limit. The results agree with calculations in Schwinger Boson mean field theory. In presence of a Kondo coupling to itinerant electrons, the model shows a phase transition from a Kondo phase to a field fluctuation dominated phase. These models are good starting points for understanding behaviour of impurities in a system near a zero-temperature magnetic transition. They are also useful for understanding the dynamical local mean field theory of Kondo lattice with Heisenberg (spin-glass type) magnetic interactions.