Kondo Effect in Bosonic Spin Liquids

In a metal, a magnetic impurity is fully screened by the conduction electrons at low temperature. In contrast, impurity moments coupled to spin-1 bulk bosons, such as triplet excitations in paramagnets, are only partially screened, even at the bulk quantum critical point. We argue that this difference is not due to the quantum statistics of the host particles but instead related to the structure of the impurity-host coupling, by demonstrating that frustrated magnets with bosonic spinon excitations can display a bosonic version of the Kondo effect. However, the Bose statistics of the bulk implies distinct behavior, such as a weak-coupling impurity quantum phase transition, and perfect screening for a range of impurity spin values. We discuss implications of our results for the compound ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$, as well as possible extensions to multicomponent bosonic gases.

Figure 1

Impurity RG flow of the bosonic Kondo model in dimension $d=2+ϵ$ (for free bulk bosons). For $ϵ>0$, the critical line crosses the $v=0$ axis, and a quantum phase transition is possible. In the presence of bulk interactions, the bulk anomalous dimension dictates the weak-coupling behavior, so that in $d=2$ Fig. (a) [(b)] applies to $\eta >1$ [$\eta <1$].

Figure 2

Schematic phase diagrams at $N=\infty$ for the Kondo problem with bosonic spinons in dimension $d=2+ϵ$.

Figure 3

Bond parameter $Q$ (lower curve) and local spin susceptibility (upper curve) as a function of temperature for $ϵ=0.5$, $S=0.3<S_c=0.5$, and $J=2.4$. Numerical calculations were done with a momentum cutoff $\Lambda =\max (k)=10$ at the bulk critical point $g=g_c$. The dashed line denotes the free Curie law $\chi =S(S+1)/T$.