Near-adiabatic parameter changes in correlated systems: Influence of the ramp protocol on the excitation energy

TL;DR

This paper investigates how the protocol of slow parameter changes affects excitation energy in correlated systems, revealing that ramp smoothness and system phase significantly influence energy decay behavior.

Contribution

It provides a detailed analysis of the influence of ramp protocols on excitation energy in the Falicov-Kimball model, connecting ramp smoothness with spectral properties and phase.

Findings

Excitation energy vanishes algebraically with ramp time, with exponents depending on phase.

Ramp smoothness affects the observable decay behavior of excitation energy.

Intrinsic spectral properties dominate the asymptotic behavior for smooth ramps.

Abstract

We study the excitation energy for slow changes of the hopping parameter in the Falicov-Kimball model with nonequilibrium dynamical mean-field theory. The excitation energy vanishes algebraically for long ramp times with an exponent that depends on whether the ramp takes place within the metallic phase, within the insulating phase, or across the Mott transition line. For ramps within metallic or insulating phase the exponents are in agreement with a perturbative analysis for small ramps. The perturbative expression quite generally shows that the exponent depends explicitly on the spectrum of the system in the initial state and on the smoothness of the ramp protocol. This explains the qualitatively different behavior of gapless (e.g., metallic) and gapped (e.g., Mott insulating) systems. For gapped systems the asymptotic behavior of the excitation energy depends only on the ramp protocol and its decay becomes faster for smoother ramps. For gapless systems and sufficiently smooth ramps the asymptotics are ramp-independent and depend only on the intrinsic spectrum of the system. However, the intrinsic behavior is unobservable if the ramp is not smooth enough. This is relevant for ramps to small interaction in the fermionic Hubbard model, where the intrinsic cubic fall-off of the excitation energy cannot be observed for a linear ramp due to its kinks at the beginning and the end.