Quantum phase transitions

TL;DR

This paper provides a pedagogical overview of quantum phase transitions, focusing on the paramagnet-to-ferromagnet transition in itinerant electrons and briefly discussing metal-insulator transitions, aiming to connect classical and quantum critical phenomena.

Contribution

It offers an accessible, lecture-based introduction to quantum phase transitions, bridging classical critical phenomena and modern quantum transition research.

Findings

Explains quantum phase transitions using the paramagnet-to-ferromagnet example

Discusses aspects of metal-insulator transitions briefly

Serves as an educational resource linking classical and quantum critical phenomena

Abstract

These are notes for lectures delivered at the NATO ASI on Dynamics in Leiden, The Netherlands, in July 1998. The main concepts relating to quantum phase transitions are explained, using the paramagnet-to-ferromagnet transition of itinerant electrons as the primary example. Some aspects of metal-insulator transitions are also briefly discussed. The exposition is strictly pedagogical in nature, with no ambitions with respect to completeness or going into technical details. The goal of the lectures is to provide a bridge between textbooks on classical critical phenomena and the current literature on quantum phase transitions. Some familiarity with the concepts of classical phase transitions is helpful, but not absolutely necessary.