Spatiotemporal Quenches in Long-Range Hamiltonians

TL;DR

This paper investigates how spatiotemporal quenches affect long-range critical Hamiltonians, revealing that optimal cooling occurs near the effective speed of excitations for certain interaction ranges, with inhomogeneous energy distributions and velocity-dependent excitation behaviors.

Contribution

It extends the understanding of spatiotemporal quenches to long-range models with power-law interactions, analyzing the effects of interaction decay on quench dynamics and excitation control.

Findings

Optimal cooling occurs when the front velocity approaches the excitation speed for  .

Energy distribution is inhomogeneous, with hot and cold regions co-propagating or counter-propagating.

Doppler cooling effects vanish for  < , with excitations governed by two relevant length scales.

Abstract

Spatiotemporal quenches are efficient at preparing ground states of critical Hamiltonians that have emergent low-energy descriptions with Lorentz invariance. The critical transverse field Ising model with nearest neighbor interactions, for instance, maps to free fermions with a relativistic low energy dispersion. However, spin models realized in artificial quantum simulators based on neutral Rydberg atoms, or trapped ions, generically exhibit long range power-law decay of interactions with $J(r) \sim 1/r^\alpha$ for a wide range of $\alpha$. In this work, we study the fate of spatiotemporal quenches in these models with a fixed velocity $v$ for the propagation of the quench front, using the numerical time-dependent variational principle. For $\alpha \gtrsim 3$, where the critical theory is suggested to have a dynamical critical exponent $z = 1$, our simulations show that optimal cooling is achieved when the front velocity $v$ approaches $c$, the effective speed of excitations in the critical model. The energy density is inhomogeneously distributed in space, with prominent hot regions populated by excitations co-propagating with the quench front, and cold regions populated by counter-propagating excitations. Lowering $\alpha$ largely blurs the boundaries between these regions. For $\alpha < 3$, we find that the Doppler cooling effect disappears, as expected from renormalization group results for the critical model which suggest a dispersion $\omega \sim q^z$ with $z < 1$. Instead, we show that excitations are controlled by two relevant length scales whose ratio is related to that of the front velocity to a threshold velocity that ultimately determines the adiabaticity of the quench.