Engineered Spacetime Quenches for Critical-State Preparation
Created about 1 month ago
ID33417
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.
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.
**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.
*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.
