Non-adiabatic preparation of critical ground states using superluminal quenches

We show that a space- and time-dependent quench protocol allows faster preparation of the ground state of critical theories than adiabatic protocols. Specifically, assuming the system initially resides in the ground state of a corresponding massive model, we show that a superluminally-moving `front' that locally quenches the mass, leaves behind it (in space) a state arbitrarily close to the ground state of the gapless model. The protocol takes time O(L) to produce the ground state of a system of size L^d (in d spatial dimensions), while a fully adiabatic protocol requires time O(L²) to produce a state with exponential accuracy in L. We present exact results for such quenches in free theories of bosons and fermions, and discuss implications for systems with interactions and ultra-violet features. Finally, we discuss results for such (and related) quenches in arbitrary conformal field theories.