Dirac criticality from field theory beyond the leading order

          @misc{ pirsa_PIRSA:22050037,
            doi = {10.48660/22050037},
            url = {https://pirsa.org/22050037},
            author = {Scherer, Michael},
            keywords = {Condensed Matter},
            language = {en},
            title = {Dirac criticality from field theory beyond the leading order},
            publisher = {Perimeter Institute},
            year = {2022},
            month = {may},
            note = {PIRSA:22050037 see, \url{https://pirsa.org}}
          }
          

Abstract

Two-dimensional gapless Dirac fermions emerge in various condensed-matter settings. In the presence of interactions such Dirac systems feature critical points and the precision determination of their exponents is a prime challenge for quantum many-body methods. In a field-theoretical language, these critical points can be described by Gross-Neveu-Yukawa-type models and in my talk I will show some results on Gross-Neveu critical behavior using field theoretical approaches beyond the leading order. To that end, I will first present higher-loop perturbative RG calculations for generic Gross-Neveu-Yukawa models and compare estimates for the exponents with recent corresponding results from Quantum Monte Carlo simulations and the conformal bootstrap. Then, I will discuss a more exotic variant of Gross-Neveu-Yukawa models which describes the interacting fractionalized excitations of two-dimensional frustrated spin-orbital magnets. Here, we have provided field-theoretical estimates for the critical exponents employing higher-order epsilon expansion, large-N calculations, and functional renormalization group.