Universal adiabatic dynamics across a quantum critical point

TL;DR

This paper investigates the behavior of quantum systems driven slowly across a critical point, revealing that excitation creation diminishes with slower changes, governed by critical exponents, supported by models like Boson Hubbard and Ising.

Contribution

It demonstrates universal scaling laws for excitation production during adiabatic crossing of quantum critical points, applicable to various models.

Findings

Excitations vanish as the process becomes infinitely slow.

Scaling of excitations follows a power law related to critical exponents.

Supported by calculations on Boson Hubbard and transverse field Ising models.

Abstract

We study temporal behavior of a quantum system under a slow external perturbation, which drives the system across a second order quantum phase transition. It is shown that despite the conventional adiabaticity conditions are always violated near the critical point, the number of created excitations still goes to zero in the limit of infinitesimally slow variation of the tuning parameter. It scales with the adiabaticity parameter as a power related to the critical exponents $z$ and $\nu$ characterizing the phase transition. We support general arguments by direct calculations for the Boson Hubbard and the transverse field Ising models.