Optimal ramp shapes for the fermionic Hubbard model in infinite dimensions

TL;DR

This paper investigates how to design optimal time-dependent interaction ramps in the fermionic Hubbard model to minimize heating, demonstrating that oscillating ramps outperform linear ones in reducing final temperatures.

Contribution

It introduces a method to determine optimal ramp shapes for the Hubbard model that significantly reduce heating compared to traditional linear ramps.

Findings

Optimal ramps are strongly oscillating with a frequency related to the bandwidth.

Optimized ramps lead to substantially lower temperatures than linear ramps.

The approach is effective even outside the perturbative regime.

Abstract

We use non-equilibrium dynamical mean field theory and a real-time diagrammatic impurity solver to study the heating associated with time-dependent changes of the interaction in a fermionic Hubbard model. Optimal ramp shapes U(t) which minimize the excitation energy are determined for an infinitesimal change. For ramp times of a few inverse hoppings, these optimal U(t) are strongly oscillating with a frequency determined by the bandwidth. We show that the scaled versions of the optimized ramps yield substantially lower temperatures than linear ramps even far outside the perturbative regime.