Speeding up critical system dynamics through optimized evolution

TL;DR

This paper investigates the fundamental limits of optimizing quantum evolution to minimize defects during phase transitions, revealing a universal timescale related to the spectral gap and classifying dynamical regimes.

Contribution

It identifies the minimal time scale for defect suppression in quantum phase transitions and links optimized dynamics to the spectral gap, providing a new understanding of non-adiabatic processes.

Findings

Minimum time for defect suppression: T ~ π/Δ

Optimal dynamics can be non-adiabatic

Classification of regimes based on action s = TΔ

Abstract

The number of defects which are generated on crossing a quantum phase transition can be minimized by choosing properly designed time-dependent pulses. In this work we determine what are the ultimate limits of this optimization. We discuss under which conditions the production of defects across the phase transition is vanishing small. Furthermore we show that the minimum time required to enter this regime is $T\sim \pi/\Delta$, where $\Delta$ is the minimum spectral gap, unveiling an intimate connection between an optimized unitary dynamics and the intrinsic measure of the Hilbert space for pure states. Surprisingly, the dynamics is non-adiabatic, this result can be understood by assuming a simple two-level dynamics for the many-body system. Finally we classify the possible dynamical regimes in terms of the action $s=T\Delta$.