Anisotropic Antiferromagnetic Heisenberg Model on a Bilayer Triangular Lattice

The antiferromagnetic Heisenberg model on the triangular lattice (AFHTL) continues to attract attention half a century after Anderson’s proposal that it might support a resonating valence bond state. The geometric frustration as well as thermal and quantum fluctuations make the AFHTL a key model for realizing unique collective phenomena, including order by disorder and various types of emergent quasi-particles. Recent studies of magnetic materials on the triangular lattice and of transition metal dichalcogenide moiré materials motivate us to study the effects of interlayer couplings on the AFHTL while remaining in two dimensions. We consider an anisotropic antiferromagnetic Heisenberg model on a bilayer triangular lattice with AA stacking. We show that the interlayer coupling along the vertical bond, although it does not introduce additional geometric frustration, enhances quantum fluctuation and destabilizes Néel order. In the strong interlayer coupling limit, the ground state becomes paramagnetic singlet dimers. Thus a spin liquid phase or a quantum critical point is expected in-between. In the strong easy-axis anisotropic (Ising) limit, we find the interlayer coupling tends to suppress the quantum fluctuations arising from a transverse magnetic field.