Dynamics of a Quantum Phase Transition and Relaxation to a Steady State

TL;DR

This paper reviews recent theoretical advances in understanding how quantum systems behave when driven across phase transitions or suddenly quenched, focusing on excitation scaling and relaxation phenomena relevant to quantum computing and ultracold atom experiments.

Contribution

It provides a systematic overview of the quantum Kibble-Zurek mechanism and recent insights into relaxation dynamics after quantum quenches, highlighting their relevance to experimental quantum systems.

Findings

Excitation scales with the power of the driving rate.

Relaxation of pure states exhibits universal features.

Implications for adiabatic quantum state preparation.

Abstract

We review recent theoretical work on two closely related issues: excitation of an isolated quantum condensed matter system driven adiabatically across a continuous quantum phase transition or a gapless phase, and apparent relaxation of an excited system after a sudden quench of a parameter in its Hamiltonian. Accordingly the review is divided into two parts. The first part revolves around a quantum version of the Kibble-Zurek mechanism including also phenomena that go beyond this simple paradigm. What they have in common is that excitation of a gapless many-body system scales with a power of the driving rate. The second part attempts a systematic presentation of recent results and conjectures on apparent relaxation of a pure state of an isolated quantum many-body system after its excitation by a sudden quench. This research is motivated in part by recent experimental developments in the physics of ultracold atoms with potential applications in the adiabatic quantum state preparation and quantum computation.