Entanglement entropy in a holographic Kondo model

Abstract

We calculate entanglement and impurity entropies in a recent holographic model of a magnetic impurity interacting with a strongly coupled system. There is an RG flow to an IR fixed point where the impurity is screened, leading to a decrease in impurity degrees of freedom. This information loss corresponds to a volume decrease in our dual gravity model, which consists of a codimension one hypersurface embedded in a BTZ black hole background in three dimensions. There are matter fields defined on this hypersurface which are dual to Kondo field theory operators. In the large N limit, the formation of the Kondo cloud corresponds to the condensation of a scalar field. The entropy is calculated according to the Ryu-Takayanagi prescription. This requires to determine the backreaction of the hypersurface on the BTZ geometry, which is achieved by solving the Israel junction conditions. We find that the larger the scalar condensate gets, the more the volume of constant time slices in the bulk is reduced, shortening the bulk geodesics and reducing the impurity entropy. This provides a new non-trivial example of an RG flow satisfying the g-theorem. Moreover, we find explicit expressions for the impurity entropy which are in agreement with previous field theory results for free electrons. This demonstrates the universality of perturbing about an IR fixed point.Dedicated to the memory of our colleague Peter Breitenlohner

The g-theorem and quantum information theory

“…Recent work in higher dimensions includes [31,32]. Moreover, it would be interesting to explore the connection with holographic results on defect entropy [9,10,[33][34][35]. Finally, if a physical realization of our free Kondo model is possible, this would provide a system where measures of quantum information quantities may be easy to perform, in particular, the role of multipartite entanglement and the Kondo cloud could be further clarified.…”

Corner contributions to holographic entanglement entropy in AdS4/BCFT3

“…Also previous works have considered the occurrence of a hypersurface in the bulk [66][67][68][69]. An interesting application of the AdS/BCFT setup has been discussed in [70,71]. The boundary conditions determining Q are crucial in the construction of [63][64][65].…”

Entanglement of heavy quark impurities and generalized gravitational entropy

“…A natural extension of these ideas is to study the effect of excitations above the vacuum state or inclusion of new degrees of freedom in the form of flavours or defects. Here it was understood that even for flavours or defects in the quenched approximation, the application of the Ryu-Takayanagi prescription [4,5] appears to require knowledge of the backreaction from the corresponding probe degrees of freedom in the dual gravitational description [10][11][12][13][14]. It has been subsequently pointed out in [15] that this procedure can be circumvented by applying the gravitational entropy method of [8] to the quenched degrees of freedom propagating in the un-backreacted gravitational backgrounds.…”