Localized - delocalized electron quantum phase transitions

TL;DR

This paper compares two theoretical frameworks for understanding quantum phase transitions, focusing on metal-insulator and quantum Hall transitions, highlighting their conceptual differences and applications.

Contribution

It provides a comparative analysis of the thermodynamic and scaling/rG-based theories of quantum phase transitions, clarifying their respective methodologies and insights.

Findings

Both theories describe quantum phase transitions effectively.

The thermodynamic approach uses partition functions.

The scaling approach employs flow diagrams and renormalization groups.

Abstract

Metal--insulator transitions and transitions between different quantum Hall liquids are used to describe the physical ideas forming the basis of quantum phase transitions and the methods of application of theoretical results in processing experimental data. The following two theoretical schemes are discussed and compared: the general theory of quantum phase transitions, which has been developed according to the theory of thermodynamic phase transitions and relies on the concept of a partition function, and a theory which is based on a scaling hypothesis and the renormalization-group concept borrowed from quantum electrodynamics, with the results formulated in terms of flow diagrams.