RKKY-induced chiral spin liquids

Chirality in spin systems relies on the Dzyaloshinskii-Moriya (DM) interaction, which is typically constrained to non-centrosymmetric systems. In heavy fermions or doped Mott insulators, the Higgs effect imparts charge to spinons, offering a means to manipulate their chirality. However, these mechanisms often prove ineffective within the Mott regime or under weak coupling between spinons and conduction electrons.

Motivated by our findings from exact diagonalization studies on small systems, we explore the possibility of inducing chirality in the spin sector through a weak Kondo coupling with conduction electrons, aided by an external magnetic field. This novel approach aims to produce a tunable DM interaction even in centrosymmetric. The weak Kondo coupling gives rise to the dynamic, long-range, and retarded Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction between spins. To address this, we employ the Sachdev-Ye formalism, particularly in the large-N limit.

Starting from spins on a honeycomb lattice, we show that breaking time-reversal symmetry in the electron sector can lead to the opening of a gap in the spin sector, resulting in the emergence of chiral edge states. To analyze this further, we study the orbital effects of an external magnetic field on the spin sector. 

Lastly, gapless spin liquids are susceptible to dimerization which breaks the translational symmetry. In addition to the hopping phase, the RKKY interaction can also modify the spinon hopping amplitudes. We analyze to what extent RKKY interaction is successful in restoring translational invariance in spin systems.