Physical Properties of Metals from a Renormalization Group Standpoint

TL;DR

This paper applies renormalization group theory and finite-size scaling to analyze the equilibrium and transport properties of metals, focusing on Fermi and Luttinger liquids, and explores deviations from these behaviors in complex materials like cuprates.

Contribution

It introduces a renormalization group framework to understand metallic properties and characterizes violations of ideal behaviors using critical indices.

Findings

Transport coefficients depend on temperature through dangerous irrelevant operators.

Characterization of Fermi and Luttinger liquid violations via critical indices.

Application of the framework to normal-state properties of cuprates.

Abstract

We derive the equilibrium and transport properties of metals using renormalization group equations and finite-size scaling. Particular attention is given to the well-known cases of Fermi and Luttinger liquids. An important subtlety is that the temperature dependence of many transport coefficients is determined by ``dangerous'' irrelevant operators. We also characterize violations of Fermi or Luttinger liquid behavior in terms of indices, analogous to the critical indices describing phase transitions. We briefly consider the normal-state properties of the cuprates from this standpoint.