Dynamical spin correlations in kagome antiferromagnets: comparison of Abrikosov fermion and Schwinger boson approaches beyond mean field

TL;DR

This study compares Abrikosov fermion and Schwinger boson approaches to understand the dynamical spin correlations in kagome antiferromagnets, revealing differences in their spectral features and emphasizing the role of many-body effects beyond mean field.

Contribution

It provides a detailed comparison of fermionic and bosonic parton theories for kagome antiferromagnets, highlighting the impact of gauge structure and many-body effects on spin dynamics.

Findings

Fermion approach shows dome-shaped spectral features.

Boson approach yields a concave-down low-energy structure.

Many-body effects reduce the spin gap and increase spectral weight.

Abstract

Quantum spin liquids exhibit fractionalized spin excitations as a consequence of strong quantum many-body effects. The kagome antiferromagnetic Heisenberg model is a promising candidate for a quantum spin-liquid ground state; however, the nature of its excitation spectrum remains controversial, particularly regarding the presence of a spin gap and the gauge structure coupled to fractional quasiparticles. To address these issues, parton approaches have been extensively employed, where spin operators are represented in terms of fermionic or bosonic quasiparticles within the Abrikosov fermion and Schwinger boson frameworks. Thus far, these approaches have been pursued independently, and it has remained unclear how the results obtained from these frameworks compare, particularly with respect to the spin dynamics and gauge structure of the kagome antiferromagnet. Here, we investigate the dynamical spin structure factor of the antiferromagnetic Heisenberg model with a Dzyaloshinskii-Moriya interaction on the kagome lattice, relevant to herbertsmithite, by employing both approaches. We find that the dynamical spin structure factor obtained from the Abrikosov fermion mean-field theory exhibits dome-shaped features, and that its continuum structure significantly depends on the gauge structure of the spin-liquid ansatz. On the other hand, the Schwinger boson mean-field theory yields a concave-down structure in the low-energy region, distinct from that obtained using the Abrikosov fermion approach. Moreover, incorporating many-body effects beyond the mean-field approximation substantially reduces the low-energy gap and enhances the low-energy spectral weight, consistent with experimental observations. Our results suggest the importance of many-body effects in the Schwinger boson theory for capturing the low-energy spin dynamics of kagome antiferromagnets.