Rise of non-perturbative effects below the upper critical dimension

          @misc{ pirsa_PIRSA:17060020,
            doi = {10.48660/17060020},
            url = {https://pirsa.org/17060020},
            author = {},
            keywords = {Other},
            language = {en},
            title = {Rise of non-perturbative effects below the upper critical dimension},
            publisher = {Perimeter Institute},
            year = {2017},
            month = {jun},
            note = {PIRSA:17060020 see, \url{https://pirsa.org}}
          }
          

Abstract

Extracting low energy universal data of quantum critical systems is a task whose difficulty increases with decreasing dimension. The increasing strength of quantum fluctuations can be tamed by using renormalization group (RG) schemes based on dimensional regularization close to the upper critical dimension of the system. By presenting a non-perturbative approach that allows the reliable extraction of the low energy universal data for the antiferromagnetic quantum critical metal in $2 \leq d < 3$-spatial dimensions, I will exemplify how an emergent non-commutativity between the low-energy limit and the dimensional limit preempts RG schemes based on dimensional regularization to access the correct low-energy universal data in integer dimensions.