Institute for Theoretical Physics, University of Cologne

Abstract: In my talk, I discuss effective models for Dirac fermions which emerge as quasi-particle excitations on the honeycomb lattice and many other condensed-matter systems. These Dirac fermions can undergo different types of quantum transitions which represent unconventional universality classes related to variants of the Gross-Neveu model. In particular, I present our perturbative renormalization group study at four-loop order. We applied the computed series for the critical exponents and their Pade approximants to several phase transitions of current interest: metal-insulator transitions of spin-1/2 and spinless fermions on the honeycomb lattice, emergent supersymmetric surface field theory in topological phases, as well as the disorder-induced quantum transition in Weyl semimetals. Comparison with the results of other analytical and numerical methods, i.e. quantum Monte Carlo simulations, the functional renormalization group and the conformal bootstrap approach, is discussed. Depending on time, I will also discuss functional RG results for the fermion-induced quantum critical points and emergent symmetries of compatible order parameters in Dirac systems.

Host: Zi Yang Meng (9331)