(Multi-)Critical Point, and Potential Realization with infinite Fractal Symmetries

          @misc{ pirsa_PIRSA:22050051,
            doi = {10.48660/22050051},
            url = {https://pirsa.org/22050051},
            author = {Xu, Cenke},
            keywords = {Condensed Matter},
            language = {en},
            title = {(Multi-)Critical Point, and Potential Realization with infinite Fractal Symmetries},
            publisher = {Perimeter Institute},
            year = {2022},
            month = {may},
            note = {PIRSA:22050051 see, \url{https://pirsa.org}}
          }
          

Abstract

In the last few years the concept of symmetry has been significantly expanded. One exotic example of the generalized symmetries, is the “type-II subsystem symmetry”, where the conserved charge is defined on a fractal sublattice of an ordinary lattice. In this talk we will discuss examples of models with the fractal symmetries. In particular, we will introduce a quantum many-body model with a “Pascal’s triangle symmetry”, which is an infinite series of fractal symmetries, including the better known Sierpinski-triangle fractal symmetry. We will also construct a gapless multicritical point with the Pascal’s triangle symmetry, where the generator of all the fractal symmetries decay with a power-law. If time permits, we will also mention a few potential experimental realizations for models with fractal symmetries.