Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model

TL;DR

This paper presents an exact solution for a transitionless quantum driving protocol across a quantum critical point in the quantum Ising model, enabling finite-rate access to the ground state despite critical slowing down.

Contribution

It introduces a method for transitionless quantum driving through a critical point in the quantum Ising model, with an auxiliary Hamiltonian that suppresses excitations.

Findings

Exact solution for transitionless driving in the quantum Ising model

Auxiliary Hamiltonian suppresses excitations during critical crossing

Interaction range influences excitation suppression

Abstract

The dynamics of a quantum phase transition is inextricably woven with the formation of excitations, as a result of the critical slowing down in the neighborhood of the critical point. We design a transitionless quantum driving through a quantum critical point that allows one to access the ground state of the broken-symmetry phase by a finite-rate quench of the control parameter. The method is illustrated in the one-dimensional quantum Ising model in a transverse field. Driving through the critical point is assisted by an auxiliary Hamiltonian, for which the interplay between the range of the interaction and the modes where excitations are suppressed is elucidated.