Fast preparation of critical ground states using superluminal fronts

Abstract

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 $\text{locally}$ quenches the mass, leaves behind it (in space) a state $\text{arbitrarily close}$ 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.

4.25 + 10 pages, 3 + 2 figures

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• Scrambling and Recovery of Quantum Information in Inhomogeneous Quenches in Two-dimensional Conformal Field Theories
• Inhomogeneous quenches as state preparation in two-dimensional conformal field theories
• Cooling arbitrary near-critical systems using hyperbolic quenches
• Engineering non-equilibrium quantum phase transitions via causally gapped Hamiltonians
• Entanglement front generated by an impurity travelling in an isolated many-body quantum system
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• The anomalously slow dynamics of inhomogeneous quantum annealing
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• Design and benchmarks for emulating Kondo dynamics on a quantum chip
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