Quantum quenches and competing orders

Abstract

We study the nonequilibrium dynamics of an electronic model of competition between an unconventional charge density wave (a bond density wave) and $d$-wave superconductivity. In a time-dependent Hartree-Fock+BCS approximation, the dynamics reduces to the equations of motion of operators realizing the generators of SU(4) at each pair of momenta, $(\mathbit{k},\ensuremath{-}\mathbit{k})$, in the Brillouin zone. We also study the nonequilibrium dynamics of a quantum generalization of a O(6) nonlinear $\ensuremath{\sigma}$ model of competing orders in the underdoped cuprates [Hayward et al., Science 343, 1336 (2014)]. We obtain results, in the large $N$ limit of a $O(N)$ model, on the time dependence of correlation functions following a pulse disturbance. We compare our numerical studies with recent picosecond optical experiments. We find that, generically, the oscillatory responses in our models share various qualitative features with the experiments.