Generic Field-Driven Phenomena in Kitaev Spin Liquids: Canted Magnetism and Proximate Spin Liquid Physics

TL;DR

This paper investigates magnetic phenomena in Kitaev spin liquids under intermediate magnetic fields, revealing generic features like spin canting and proximate spin liquid regimes, using numerical and analytical methods across different lattice models.

Contribution

It provides a comprehensive numerical and analytical study of intermediate-field magnetic phenomena in Kitaev models, highlighting the emergence of canted magnetism and stable spin liquid phases.

Findings

Antiferromagnetic Kitaev models stabilize spin liquid phases at intermediate fields.

Intermediate regimes exhibit significant spin canting and antiferromagnetic correlations.

Symmetry obstructions prevent canted magnetism in certain honeycomb models without symmetry breaking.

Abstract

Topological spin liquids in two spatial dimensions are stable phases in the presence of a small magnetic field, but may give way to field-induced phenomena at intermediate field strengths. Sandwiched between the low-field spin liquid physics and the high-field spin-polarized phase, the exploration of magnetic phenomena in this intermediate regime however often remains elusive to controlled analytical approaches. Here we numerically study such intermediate-field magnetic phenomena for two representative Kitaev models (on the square-octagon and decorated honeycomb lattice) that exhibit either Abelian or non-Abelian topological order in the low-field limit. Using a combination of exact diagonalization and density matrix renormalization group techniques, as well as linear spin-wave theory, we establish the generic features of Kitaev spin liquids in an external magnetic field. While ferromagnetic models typically exhibit a direct transition to the polarized state at a relatively low field strength, antiferromagnetic couplings not only substantially stabilizes the topological spin liquid phase, but generically lead to the emergence of a distinct field-induced intermediate regime, separated by a crossover from the high-field polarized regime. Our results suggest that, for most lattice geometries, this regime generically exhibits significant spin canting, antiferromagnetic spin-spin correlations, and an extended proximate spin liquid regime at finite temperatures. Notably, we identify a symmetry obstruction in the original honeycomb Kitaev model that prevents, at least for certain field directions, the formation of such canted magnetism without breaking symmetries -- consistent with the recent numerical observation of an extended gapless spin liquid in this case.