Minimal action shortcut to adiabaticity in a driven Kitaev chain: competing gaps in a topological transition at finite-time

TL;DR

This paper applies a minimal action shortcut to adiabaticity (MA-STA) to a Kitaev chain, enabling fast, high-fidelity topological phase transitions despite symmetry sector gap closures.

Contribution

It introduces a multi-step MA-STA protocol for the Kitaev chain, achieving efficient control across topological phases with reduced transition times.

Findings

High fidelities achieved with MA-STA at shorter times than linear ramps.

MA-STA suppresses work fluctuations more effectively than linear protocols.

The approach guides control design in many-body systems with competing energy scales.

Abstract

One of the main difficulties in preparing many-body ground states is achieving the target state through simple counterdiabatic controls. For critical systems crossing a transition to a topological phase, this task becomes even more challenging due to the closing of the gaps in multiple symmetry sectors. This is the case of the Kitaev chain, whose transition between the trivial and topological phases involves states belonging to different symmetry sectors. In this work, we apply the recently introduced minimal action shortcut to adiabaticity (MA-STA) to a Kitaev chain and propose a multi-step strategy to obtain the optimal control protocol to drive the system across its different phases. Our results show that high fidelities can be achieved through the adapted MA-STA at time scales much shorter than those of linear ramp protocols. We also compare the performance of both controls in suppressing work fluctuations. These findings may guide the design of STA protocols in many-body systems where competing energy scales and symmetries shape the global dynamics.