Competing orders, the Wess-Zumino-Witten term, and spin liquids

TL;DR

This paper explores how the Wess-Zumino-Witten term in frustrated magnets with competing orders can lead to the emergence of spin liquids with fractionalized excitations, bridging traditional and parton-based theories.

Contribution

It demonstrates that the WZW term can induce spin liquids in frustrated magnets without fractionalized particles, linking Ginzburg-Landau-Wilson theory to spin liquid physics.

Findings

Spin liquids can arise from competing orders intertwined by a WZW term.

Intermediate phases break certain symmetries during vortex condensation.

Results align with parton theory predictions without fractionalized particles.

Abstract

In this paper, we demonstrate that in frustrated magnets when several conventional (i.e., symmetry-breaking) orders compete, and are "intertwined" by a Wess-Zumino-Witten (WZW) term, the possibility of spin liquid arises. The resulting spin liquid could have excitations which carry fractional spins and obey non-trivial self/mutual statistics. As a concrete example, we consider the case where the competing orders are the N\'{e}el and valence-bond solid (VBS) order on square lattice. Examining different scenarios of vortex condensation from the VBS side, we show that the intermediate phases, including spin liquids, between the N\'{e}el and VBS order always break certain symmetry. Remarkably, our starting theory, without fractionalized particles (partons) and guage field, predicts results agreeing with those derived from a parton theory. This suggests that the missing link between the Ginzberg-Landau-Wilson action of competing order and the physics of spin liquid is the WZW term.