Sub-ohmic two-level system representation of the Kondo effect

TL;DR

This paper demonstrates that the Kondo effect can be modeled as a two-level system coupled to a sub-ohmic environment, revealing spontaneous symmetry breaking linked to Kondo coherence, using numerical methods to explore quantum fluctuations.

Contribution

It proves that the slave-spin in the Anderson impurity model behaves like a two-level system with a sub-ohmic environment, connecting symmetry breaking to Kondo physics.

Findings

Slave-spin acts as a two-level system coupled to a sub-ohmic bath.

Spontaneous Z2 symmetry breaking occurs at zero temperature.

Kondo temperature is proportional to the square of the order parameter.

Abstract

It has been recently shown that the particle-hole symmetric Anderson impurity model can be mapped onto a $Z_2$ slave-spin theory without any need of additional constraints. Here we prove by means of Numerical Renormalization Group that the slave-spin behaves in this model like a two-level system coupled to a sub-ohmic dissipative environment. It follows that the $Z_2$ symmetry gets spontaneously broken at zero temperature, which we find can be identified with the on-set of Kondo coherence, being the Kondo temperature proportional to the square of the order parameter. Since the model is numerically solvable, the results are very enlightening on the role of quantum fluctuations beyond mean field in the context of slave-boson approaches to correlated electron models, an issue that has been attracting interest since the 80's. Finally, our results suggest as a by-product that the paramagnetic metal phase of the Hubbard model at half-filling, in infinite coordination lattices and at zero temperature, as described for instance by Dynamical Mean Field Theory, corresponds to a slave-spin theory with a spontaneous breakdown of a local $Z_2$ gauge symmetry.