Ramp and periodic dynamics across non-Ising critical points

TL;DR

This paper investigates the dynamics of ultracold bosons in a 1D optical lattice near quantum critical points, analyzing ramp and periodic drives through numerical simulations and uncovering scaling laws and dynamical freezing phenomena.

Contribution

It provides the first detailed numerical analysis of ramp and periodic dynamics across non-Ising quantum critical points in 1D bosonic systems, revealing Kibble-Zurek scaling and many-body Stuckelberg interference.

Findings

Kibble-Zurek scaling observed in excitation density and excess energy.

Near-perfect dynamical freezing at specific drive frequencies.

Scaling behavior consistent with q-state Potts universality class.

Abstract

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 wavefunction 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 $Q$ shows 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 periodic protocol, we show that the model display near-perfect dynamical freezing at specific frequencies; at these frequencies $D, Q \to 0$ and $|F| \to 1$. 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.