Quantum Criticality: Gauge Fields and Matter

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.

The Thirring Model is a covariant quantum field theory of interacting fermions, sharing many features in common with effective theories of two-dimensional electronic systems with linear dispersion such as graphene. For a small number of flavors and sufficiently strong interactions the ground state may be disrupted by condensation of particle- hole pairs leading to a quantum critical point. With no small dimensionless parameters in play in this regime the Thirring model is plausibly the simplest theory of fermions requiring a numerical solution. I will review what is currently known focussing on recent results and challenges from simulations employing Domain Wall Fermions, a formulation drawn from state-of-the-art lattice QCD, to faithfully capture the underlying symmetries at the critical point.