Inhomogeneous quasi-adiabatic driving of quantum critical dynamics in weakly disordered spin chains

TL;DR

This paper proposes an inhomogeneous quasi-adiabatic driving protocol for weakly disordered quantum spin chains that significantly reduces residual energy during quantum phase transitions, outperforming traditional homogeneous methods.

Contribution

It introduces an inhomogeneous control scheme that optimizes adiabatic dynamics in disordered spin chains, demonstrating superior residual energy suppression.

Findings

Residual energy depends nonmonotonically on the inhomogeneity length scale and sweep velocity.

Optimal conditions for residual energy suppression are identified.

Inhomogeneous driving can outperform homogeneous control fields by several orders of magnitude.

Abstract

We introduce an inhomogeneous protocol to drive a weakly disordered quantum spin chain quasi-adiabatically across a quantum phase transition and minimize the residual energy of the final state. The number of spins that simultaneously reach the critical point is controlled by the length scale in which the magnetic field is modulated, introducing an effective size that favors adiabatic dynamics. The dependence of the residual energy on this length scale and the velocity at which the magnetic field sweeps out the chain is shown to be nonmonotonic. We determine the conditions for an optimal suppression of the residual energy of the final state and show that inhomogeneous driving can outperform conventional adiabatic schemes based on homogeneous control fields by several orders of magnitude.