We study ramp and periodic dynamics of ultracold bosons in an one-dimensional (1D) optical lattice which supports quantum critical points separating a uniform and a $Z_3$ or $Z_4$ symmetry broken density-wave ground state. Our protocol involves both linear and periodic drives which takes the system from the uniform state to the quantum critical point (for linear drive protocol) or to the ordered state and back (for periodic drive protocols) via controlled variation of a parameter of the system Hamiltonian. We provide exact numerical computation, for finite-size boson chains with $L\le 24$ using exact diagonalization (ED), of the excitation density $D$, the wave function overlap $F$, and the excess energy $Q$ at the end of the drive protocol. For the linear ramp protocol, we identify the range of ramp speeds for which $D$ and $Q$ show Kibble-Zurek scaling. We find, based on numerical analysis with $L\le 24$, that such scaling is consistent with that expected from critical exponents of the $q$-state Potts universality class with $q=3,4$. For the periodic protocol, we show that the model displays near-perfect dynamical freezing at specific frequencies; at these frequencies $D,Q\to 0$ and $\left|F\right|\to 1$. We provide a semi-analytic explanation of such freezing behavior and relate this phenomenon to a many-body version of Stuckelberg interference. We suggest experiments which can test our theory.

• Received 16 November 2017
• Revised 10 January 2018

DOI:https://doi.org/10.1103/PhysRevB.97.014309