Fast preparation of critical ground states using superluminal fronts

We propose a spatio-temporal quench protocol that allows for the fast preparation of ground states of gapless models with Lorentz invariance. Assuming the system initially resides in the ground state of a corresponding massive model, we show that a superluminally-moving `front' that $\textit{locally}$ quenches the mass, leaves behind it (in space) a state $\textit{arbitrarily close}$ to the ground state of the gapless model. Importantly, our protocol takes time $\mathcal{O} \left( L \right)$ to produce the ground state of a system of size $\sim L^d$ ($d$ spatial dimensions), while a fully adiabatic protocol requires time $\sim \mathcal{O} \left( L^2 \right)$ to produce a state with exponential accuracy in $L$. The physics of the dynamical problem can be understood in terms of relativistic rarefaction of excitations generated by the mass front. We provide proof-of-concept by solving the proposed quench exactly for a system of free bosons in arbitrary dimensions, and for free fermions in $d = 1$. We discuss the role of interactions and UV effects on the free-theory idealization, before numerically illustrating the usefulness of the approach via simulations on the quantum Heisenberg spin-chain.