Critical Behavior of CP^1 at theta = pi, Haldane's Conjecture and the Universality Class

TL;DR

This paper investigates the critical behavior of the CP^1 model at theta=pi, confirming Haldane's conjecture outside strong coupling, and finds the critical line exhibits continuously varying exponents, differing from the WZNW model class.

Contribution

The study applies a novel approach to analyze theta dependence, revealing the universality class of the critical line differs from the expected WZNW model.

Findings

Haldane's conjecture is verified outside the strong coupling regime.

The critical line does not belong to the WZNW model universality class.

Critical exponents vary continuously along the critical line.

Abstract

Using an approach to analyze the theta dependence of systems with a theta-term we recently proposed, the critical behavior of CP^1 at theta=pi is studied. We find a region outside the strong coupling regime where Haldane's conjecture is verified. The critical line however does not belong to the universality class of the Wess-Zumino-Novikov-Witten model at topological coupling k=1 since it shows continuously varying critical exponents.