Many-body spin Berry phases emerging from the $\pi$-flux state: antiferromagnetic/valence-bond-solid competition

TL;DR

This paper explores the topological features of the $\pi$-flux state in 2+1D Heisenberg antiferromagnets, revealing the interplay between antiferromagnetic and valence-bond-solid orders and deriving an effective theory with Berry phases.

Contribution

It introduces a new effective theory for $\pi$-flux states that captures the competition between AF and VBS orders and includes Berry phases related to monopoles.

Findings

Derived an effective theory with Wess-Zumino-Witten-like term.

Reproduced Haldane's hedgehog Berry phases.

Generalized the theory to all dimensions for $\pi$-flux states.

Abstract

We uncover new topology-related features of the $\pi$-flux saddle-point solution of the $D$=2+1 Heisenberg antiferromagnet. We note that symmetries of the spinons sustain a built-in competition between antiferromagnetic (AF) and valence-bond-solid (VBS) orders, the two tendencies central to recent developments on quantum criticality. An effective theory containing an analogue of the Wess-Zumino-Witten term is derived, which generates quantum phases related to AF monopoles with VBS cores, and reproduces Haldane's hedgehog Berry phases. The theory readily generalizes to $\pi$-flux states for all $D$.