The path to emergent symmetries induced by strong disorder
A common theme in low- or high-energy physics is the fact that a state may have a symmetry lower than its underlying Hamiltonian/Lagrangian. Behind this feature is the phenomenon of spontaneous symmetry breaking. A far less common situation corresponds to a low-energy state whose symmetry is *greater* than its underlying Lagrangian. The most famous example is the critical 2D Ising model in a small magnetic field, which has an emergent (and ill-understood) $E_8$ symmetry. Other examples have been found in the last several years in clean systems. Recently, we have shown that strong disorder can be the driving force to an emergent symmetry: strongly disordered spin-1 chains with manifest SU(2) symmetry show an emergent SU(3) symmetry in two different phases. It was not clear, however, whether this was just an isolated example. It is not: we will show that other disordered systems have a similar pattern of emergent behavior, with rich phase diagrams.