2018 · Fast Preparation of Critical Ground States Using Superluminal Fronts

Paper focus: Agarwal, Bhatt, and Sondhi, Fast Preparation of Critical Ground States Using Superluminal Fronts (2018). This paper proposes preparing an extended low-energy region by shaping where a quench creates and sends excitations. It is best read as a resource-and-geometry argument: identify the easy initial state, the moving control pattern, the region whose quality matters, and the hot excitations left elsewhere. The fronts page compares the approach with other state-preparation methods. 1

Figure to read

A moving front populates different propagation directions unequally. Figure 1 in the source paper. Bernier, Simon; Agarwal, Kartiek. Spatiotemporal quenches for efficient critical ground state preparation in the two-dimensional transverse field Ising model, Physical Review B 111, 054311 (2025). Paper. CC BY 4.0. Original manuscript graphic; no alterations.

Read the arrows as excitation trajectories, not as the velocity of the control pattern. Compare the cold modes behind the front with the hotter modes traveling alongside it; this is why local preparation quality and total sample energy are different tests.

What is being prepared?

The target is a gapless model with an approximately Lorentz-invariant low-energy description. The starting point is a related gapped model whose ground state is assumed easier to prepare. A moving front locally removes the mass or gap parameter. The key output is a large region approaching the target ground-state behavior, rather than a claim that no excitations are generated anywhere. This spatial qualification is essential to the protocol's interpretation. 1

Conventional adiabatic evolution becomes difficult near a closing gap because avoiding transitions requires increasingly long times. Adiabatic perturbation theory supplies a useful benchmark and explains why a finite-rate uniform ramp excites critical modes. However, a comparison of runtimes must specify the error measure: matching excess energy, correlation functions, and global fidelity can give different resource requirements. 2

Why a faster-than-light front can cool

Here “light” means the emergent propagation velocity of the low-energy model. A spacetime-dependent control pattern can move faster than that velocity. Excitations generated by the front have direction-dependent Doppler shifts. Modes moving with the front can carry substantial energy into a relatively narrow hot region, while oppositely moving or transverse modes populate the useful region more weakly. In the idealized limit, the cold region can approach vacuum-like behavior. 1

No microscopic cooling bath is required by that ideal construction, and unitary evolution does not reduce the entropy of the entire isolated system. Instead, the spatial arrangement of energy and correlations changes. This is why the protocol should be evaluated using spatially resolved observables. A global average can obscure both the benefit in the useful region and the cost in the discarded or subsequently managed hot region.

What the calculations establish

The paper analyzes free-field examples and includes a numerical illustration in a Heisenberg spin chain. These serve different purposes: exact calculations expose the mechanism, while the interacting lattice example tests whether it remains useful beyond the simplest continuum theory. The proposed favorable size scaling is conditional on the assumptions and accuracy comparison used in the paper. It should not be read as a universal complexity bound for arbitrary state preparation. 1

Figure 1 of the original paper organizes the causal picture. The later two-dimensional illustration reproduced here makes the directional population of modes especially clear. When reading either, distinguish the moving control front from the trajectories of physical excitations. Their velocities play different roles. Also identify the time at which the state is assessed, since subsequent propagation can bring hot excitations back into a region that was initially cold. 3

Subsequent tests and complementary methods

Hyperbolic quenches use a different trajectory to exploit conformal constraints in one dimension. Long-range Ising simulations test what happens when dispersion departs from the relativistic assumption. Two-dimensional Ising calculations then examine an interacting geometry with different numerical limitations. Together these extensions define a research program of testing the mechanism's boundaries, rather than merely repeating its ideal argument. 4 5 3

The wider shortcuts-to-adiabaticity literature offers competing controls, sometimes requiring auxiliary operators or stronger prior knowledge of the spectrum. 6 A useful experimental benchmark would hold runtime, addressing resolution, and initial-state quality fixed, then compare energy and correlations inside the same target region. The unresolved practical question is whether a favorable ideal scaling remains advantageous once finite temperature, boundary reflections, and imperfect control are included. The geometry page explains why those effects are central to the physics rather than minor implementation details.

References

1. Agarwal, Kartiek; Bhatt, R. N.; Sondhi, S. L.. Fast Preparation of Critical Ground States Using Superluminal Fronts. Physical Review Letters 120, 210604 (2018). Open manuscript.
2. De Grandi, C.; Polkovnikov, A.. Adiabatic perturbation theory: from Landau-Zener problem to quenching through a quantum critical point. "Quantum Quenching, Annealing and Computation", Eds. A. Das, A. Chandra and B. K. Chakrabarti, Lect. Notes in Phys., vol. 802 (Springer, Heidelberg 2010). Open manuscript.
3. Bernier, Simon; Agarwal, Kartiek. Spatiotemporal quenches for efficient critical ground state preparation in the two-dimensional transverse field Ising model. Physical Review B 111, 054311 (2025). Open manuscript.
4. Mitra, Prahar; Ippoliti, Matteo; Bhatt, R. N.; Sondhi, S. L.; Agarwal, Kartiek. Cooling arbitrary near-critical systems using hyperbolic quenches. Physical Review B 99, 104308 (2019). Open manuscript.
5. Bernier, Simon; Agarwal, Kartiek. Spatiotemporal Quenches in Long-Range Hamiltonians. Physical Review B 108, 024310 (2023). Open manuscript.
6. Guéry-Odelin, D.; Ruschhaupt, A.; Kiely, A.; Torrontegui, E.; Martínez-Garaot, S.; Muga, J. G.. Shortcuts to adiabaticity: concepts, methods, and applications. Rev. Mod. Phys. 91, 045001 (2019). Open manuscript.

Independent research synthesis. Literature checked 5 September 2026; preprints are identified in the references.