Shortcut to Adiabaticity in the Lipkin-Meshkov-Glick Model

TL;DR

This paper develops a hybrid control strategy combining shortcuts to adiabaticity and optimal control to effectively suppress defects during phase transitions in the Lipkin-Meshkov-Glick model, despite the infinite correlation length and critical gap closing.

Contribution

It introduces a novel hybrid approach that enhances transitionless quantum driving in many-body systems with critical points.

Findings

Effective suppression of defect production across the phase transition.

Hybrid strategy outperforms traditional methods in complex many-body systems.

Applicable to systems with infinite correlation length and critical gap closing.

Abstract

We study transitionless quantum driving in an infinite-range many-body system described by the Lipkin-Meshkov-Glick model. Despite the correlation length being always infinite the closing of the gap at the critical point makes the driving Hamiltonian of increasing complexity also in this case. To this aim we develop a hybrid strategy combining shortcut to adiabaticity and optimal control that allows us to achieve remarkably good performance in suppressing the defect production across the phase transition.