On the origin of the quantum-critical transition in the bilayer Heisenberg model

TL;DR

This paper investigates the quantum-critical transition in the bilayer Heisenberg model, revealing that the transition occurs within the ordered phase due to divergence of the coupling constant, using a novel coherent state approach.

Contribution

The study introduces a new coherent state framework to analyze the transition, mapping it onto the quantum non-linear sigma model and clarifying the transition's nature.

Findings

The bare coupling constant diverges at the classical transition.

The quantum transition occurs inside the classical ordered phase.

A new coherent state approach is developed for analysis.

Abstract

The bilayer Heisenberg antiferromagnet is known to exhibit a quantum-critical transition at a particular value of the inter-layer coupling. Using a new type of coherent state, appropriate to the special order parameter structure of the bilayer, we map the problem onto the quantum non-linear sigma model. It is found that the bare coupling constant diverges at the classical transition of Chubukov and Morr, so that in any finite dimension the actual transition occurs inside the ordered phase of the classical theory.