Magnetic fragmentation and fractionalized Goldstone modes in a bilayer quantum spin liquid

TL;DR

This paper explores a bilayer quantum spin liquid with Kitaev interactions, revealing a magnetic fragmentation transition, emergent gauge fields, and fractionalized Goldstone modes, advancing understanding of complex quantum phases.

Contribution

It introduces a novel bilayer quantum spin liquid model with Kitaev interactions, identifying a magnetic fragmentation transition and fractionalized Goldstone modes, supported by field theory and perturbative analysis.

Findings

Identification of a magnetic fragmentation transition.

Emergence of non-local string order parameters.

Existence of fractionalized, non-local Goldstone modes.

Abstract

We study the phase diagram of a bilayer quantum spin liquid model with Kitaev-type interactions on a square lattice. We show that the low energy limit is described by a $\pi$-flux Hubbard model with an enhanced SO(4) symmetry. The antiferromagnetic Mott transition of the Hubbard model signals a magnetic fragmentation transition for the spin and orbital degrees of freedom of the bilayer. The fragmented "N\'eel order" features a non-local string order parameter for an in-plane N\'eel component, in addition to an anisotropic local order parameter. The associated quantum order is characterized by an emergent $\mathbb{Z}_{2} \times \mathbb{Z}_{2}$ gauge field when the N\'eel vector is along the $\hat{z}$ direction, and a $\mathbb{Z}_2$ gauge field otherwise. We underpin these results with a perturbative calculation, which is consistent with the field theory analysis. We conclude with a discussion on the low energy collective excitations of these phases and show that the Goldstone boson of the $\mathbb{Z}_{2} \times \mathbb{Z}_{2}$ phase is fractionalized and non-local.