Optimal non-linear passage through a quantum critical point

TL;DR

This paper investigates how to optimally traverse a quantum critical point with minimal defects, revealing that a power-law tuning minimizes excitations, with the optimal power linked to passage time and critical exponents.

Contribution

It introduces a universal optimal power-law protocol for adiabatic passage through quantum critical points, supported by scaling analysis and model calculations.

Findings

Optimal tuning follows a power-law in time.

Optimal power depends on passage time and critical exponents.

Supports results with Ising model calculations.

Abstract

We analyze the problem of optimal adiabatic passage through a quantum critical point. We show that to minimize the number of defects the tuning parameter should be changed as a power-law in time. The optimal power is proportional to the logarithm of the total passage time multiplied by universal critical exponents characterizing the phase transition. We support our results by the general scaling analysis and by explicit calculations for the transverse field Ising model.