Kondo spin liquid in Kondo necklace model: Classical disordered phase versus symmetry-protected topological state

TL;DR

This paper explores the topological properties of Kondo spin liquid phases in one- and two-dimensional Kondo necklace models, revealing connections to Haldane phases and symmetry-protected topological states through nonlinear sigma models.

Contribution

It demonstrates that the Kondo spin liquid phase can exhibit topological features akin to SPT states, linking microscopic models to topological field theories.

Findings

One-dimensional Kondo spin liquid resembles the Haldane phase.

Two-dimensional models map onto O(4)-like NLSM with O(3) anisotropy.

Inclusion of defects and symmetry considerations relate to SPT states.

Abstract

We study possible topological features of Kondo spin liquid phase in terms of the one- and two-dimensional Kondo necklace models within the frame work of quantum O(N) non-liner sigma model (NLSM). In the one-dimensional case, it is found that the bulk properties of the Kodno spin liquid phase are similar to the well-known Haldane phase at strong coupling fixed point. The difference between them mainly comes from their boundaries due to the effect of the topological term. In the two-dimensional case, the system can be mapped onto an O(4)-like NLSM with some O(3) anisotropy. Interestingly, we find that if hedgehog-like point defects are included together with the restoration of the full O(4) symmetry, our model is identical to a kind of SU(2) symmetry-protected topological (SPT) state. Additionally, if the system has the O(5) symmetry instead, the effective NLSM with Wess-Zumino-Witten term is just a description of the surface modes of a three-dimensional SPT state, though such O(5) NLSM could not be a proper description of Kondo spin liquid phase due to its gaplessness. We expect that the discussions might provide useful threads to identify certain microscopic bilayer antiferromagnet models (and related materials), which can support the desirable SPT states.