Breakdown of Landau-Ginzburg-Wilson theory for certain quantum phase transitions

TL;DR

This paper demonstrates that the traditional Landau-Ginzburg-Wilson theory fails for certain quantum ferromagnetic transitions due to singular couplings, resulting in unique scaling behaviors in specific dimensions.

Contribution

It reveals the breakdown of the Landau-Ginzburg-Wilson framework for quantum ferromagnetic transitions and derives the exact scaling behavior caused by long-range interactions.

Findings

Landau-Ginzburg-Wilson theory breaks down for certain quantum phase transitions.

Singular coupling induces long-range interactions between spins.

Exact scaling behavior determined for 1<d≤3 dimensions.

Abstract

The quantum ferromagnetic transition of itinerant electrons is considered. It is shown that the Landau-Ginzburg-Wilson theory described by Hertz and others breaks down due to a singular coupling between fluctuations of the conserved order parameter. This coupling induces an effective long-range interaction between the spins of the form 1/r^{2d-1}. It leads to unusual scaling behavior at the quantum critical point in $1<d\leq 3$ dimensions, which is determined exactly.