Dynamics of a Quantum Phase Transition

TL;DR

This paper compares two methods for analyzing the dynamics of quantum phase transitions in the Ising model, demonstrating their compatibility and providing insights into defect formation during quenches.

Contribution

It introduces and compares a standard thermodynamic approach and a quantum Landau-Zener based approach to quantum phase transition dynamics.

Findings

Both approaches produce compatible scaling laws for defect density.

The methods reveal similar insights into the dynamics of quantum phase transitions.

The study enhances understanding of defect formation during quantum quenches.

Abstract

We present two approaches to the dynamics of a quench-induced phase transition in quantum Ising model. The first one retraces steps of the standard approach to thermodynamic second order phase transitions in the quantum setting. The second one is purely quantum, based on the Landau-Zener formula for transition probabilities in avoided level crossings. We show that the two approaches yield compatible results for the scaling of the defect density with the quench rate. We exhibit similarities between them, and comment on the insights they give into dynamics of quantum phase transitions.