New phase transitions and singularities in quasiperiodic quantum Ising chains

Unlike random or periodic potentials, quasi-periodic modulation can induce localisation-delocalisation transitions in one dimension. In this talk we analyse the implications of this for symmetry breaking in the quasi-periodically modulated quantum Ising model in 1D.

Though weak quasi-periodic modulation is irrelevant, we show strong modulation induces new ferromagnetic and paramagnetic phases which are fully localised and gapless. The quasi-periodic potential and localised excitations lead to quantum criticality that is intermediate to that of the clean and randomly disordered models. We numerically calculate the associated exponents and analytically investigate the stability of the transition to a large family of perturbations that preserve the quasi-periodic structure of the model.