Nicolas Paris & Sankarshan Sahu

Salle 523, couloir 12-13, 5è étage

Nicolas Paris : Non-perturbative solution of the three-channel Kondo (3CK) model

In 1964, Kondo explained the resistivity minimum in dilute magnetic alloys as a result of conduction electrons screening localized magnetic moments. This behavior is captured by the simple yet profound Kondo model—a single spin interacting with s-wave conduction electrons—which became a key model in strongly correlated electron physics and was later solved using Wilson’s Numerical Renormalization Group.

In this talk, I will present the three-channel Kondo (3CK) model, where three electron channels compete to screen a single impurity spin. Recently realized experimentally by Iftikhar et al. (Science, 2018), the 3CK model provides a minimal setting to explore quantum criticality and non-Fermi liquid behavior. I will show how the Non-Perturbative Functional Renormalization Group offers valuable theoretical insight into this rich and unconventional physics.

Sankarshan Sahu : Towards a generalization of the Central Limit Theorem to critical systems

The Central Limit Theorem does not hold for strongly correlated stochastic variables, as is the case for statistical systems close to criticality. Recently, the calculation of the probability distribution function (PDF) of the magnetization mode at criticality has been performed with the functional renormalization group in the case of the three-dimensional Ising model. It has been shown that there exists an entire family of universal PDFs parameterized by \(\zeta=\lim_{L,\xi_\infty\rightarrow\infty}L/\xi_\infty\) which is the ratio of the system size \(L\) to the bulk correlation length \(\xi_{\infty}\) with \(L,\xi_{\infty}\to\infty\). We compute the whole family of these universal PDFs at both one and two loop orders in perturbation theory and show that the agreement with Monte-Carlo simulations becomes quantitative at two loops.