# Engineered Spacetime Quenches for Critical-State Preparation
⏎
**Anchor paper:** K. Agarwal, R.N. Bhatt, S.L. Sondhi, "Fast preparation of critical ground states using superluminal fronts," *Phys. Rev. Lett.* 120, 210604 (2018). [arXiv:1710.09840]
⏎
## Background
Preparing the ground state of a critical (gapless) many-body system by adiabatic evolution is fundamentally slow: the adiabatic theorem requires evolution times scaling at least as L² (system size squared) for exponential accuracy, and finite-rate quenches through a vanishing gap inevitably generate Kibble-Zurek excitations. No transparent, scalable prescription existed for driving a macroscopic system to its critical ground state in time scaling only linearly with system size. Open question: could a spatially local "quench front" — separating an already-gapped region from a still-evolving critical region, moving faster than the emergent light-cone velocity — exploit relativistic-like kinematics to sweep excitations away?
⏎
## New results
Starting from a gapped ground state and sweeping a mass-quenching front through the system at superluminal speed leaves behind, in its wake, a state arbitrarily close to the true critical ground state. The mechanism is a relativistic rarefaction/Doppler effect: because the front outruns the quasiparticles, excitations are red-shifted away and compress into a shrinking boundary layer near the front. Exact solutions for free bosons/fermions and t-DMRG on the Heisenberg chain confirm it: residual energy above the ground state drops from ~20% to ~0.6% of the bandwidth compared to a linear ramp, with total preparation time scaling as O(L) — a full power of L faster than adiabatic preparation.
⏎
![Superluminal front and residual excitation energy](https://ar5iv.labs.arxiv.org/html/1710.09840/assets/figreal.png)
*Fig. 3 — energy per phonon mode vs. front speed, and t-DMRG results on the Heisenberg chain showing residual excitation energy dropping sharply once the front becomes superluminal.*
⏎
## Related work in this direction
- K. Agarwal, P. Mitra, M. Ippoliti, R.N. Bhatt, S.L. Sondhi, "Cooling arbitrary near-critical systems using hyperbolic quenches," PRB 99, 104308 (2019) — generalizes the front idea to a broader "hyperbolic quench" cooling protocol.
- K. Agarwal, S. Bernier, "Spatiotemporal quenches in long-range Hamiltonians," PRB 108, 024310 (2023), and "Spatiotemporal quenches for efficient critical ground state preparation in the two-dimensional transverse field Ising model," PRB 111, 054311 (2025) — extend the engineered-front approach to long-range interactions and to 2D.
⏎
**Chiral Prethermalization in Split Condensates** is nested here: a related but distinct question about what naturally happens (rather than what's engineered to happen) after a fast, front-like perturbation splits a 1D condensate.
⏎
⏎
# Parents
⏎
* Nonequilibrium Protocols & Wavefront Engineering⏎