Holographic impurities and Kondo effect

TL;DR

This work presents a holographic, large-N model of a magnetic impurity that captures the essential physics of the Kondo effect, including impurity screening and a finite-temperature phase transition. The impurity is realized as a 1+1D defect in AdS3 with a scalar and a gauge field enabling a double-trace Kondo coupling, producing a transition at Tc ~ 0.9 TK from a normal to a condensed phase. Entanglement entropy is used to define the impurity entropy and extract the Kondo screening length ξK, with the g-theorem satisfied holographically through the defect's energy conditions. The geometric interpretation of screening and the robust qualitative agreement with large-N field theory highlight the model's usefulness for exploring impurities in strongly coupled systems and possible extensions to multi-impurity or quenched dynamics.

Abstract

Magnetic impurities are responsible for many interesting phenomena in condensed matter systems, notably the Kondo effect and quantum phase transitions. Here we present a holographic model of a magnetic impurity that captures the main physical properties of the large-spin Kondo effect. We estimate the screening length of the Kondo cloud that forms around the impurity from a calculation of entanglement entropy and show that our results are consistent with the g-theorem.

Figures (9)

• Figure 1: Raise of the resistivity at low temperatures. Points and crosses are experimental results for iron impurities in gold, while lines are theoretical predictions (figure from Kondo01071964).
• Figure 2: A cartoon of the phase diagram in heavy fermion compounds. As the parameter $\delta$ is varied at zero temperature, there is a transition from an antiferromagnetic state (AF) to a Fermi liquid of heavy fermions. The quantum critical point is at $\delta=\delta_c$, but in this case it is depicted cloaked by a superconducting dome. At low temperatures around the critical point, the system behaves like a Non-Fermi liquid. The dotted and dashed lines indicate the temperature for the transition due to RKKY interactions and the Kondo temperature, respectively (figure from phaseHF ).
• Figure 3: Holographic model of a magnetic impurity. In the gravity side the impurity is a defect extending between the boundary and the horizon. The spin current, the charge of the slave fermions and the operator ${\cal O}$ are mapped to gauge fields and a scalar field respectively (Figure from Erdmenger:2015spo).
• Figure 4: For $T<T_c$ the the vev of the operator ${\cal O}$ is nonzero. The solid red line fits numerical data to $0.3(1-T/T_c)^{1/2}$. The phase transition is second order and of mean field type (Figure from Erdmenger:2013dpa).
• Figure 5: Profile of the defect for a fixed representation of the impurity spin and different temperatures $T\leq T_c$. As ${\left\langle {\cal O} \right\rangle}$ increases for lower temperatures, the profile moves to the right (Figure from Erdmenger:2015spo).