Plaquette crystal order in the triangular-lattice J₁-J₂ Heisenberg antiferromagnet and related models

The triangular-lattice Heisenberg antiferromagnet (TLHA) is a deceptively simple model exhibiting rich physics, especially with the addition of next-nearest-neighbor (J₂) couplings. Although the decades-long debate as to the nature of the J₂=0 ground state has largely been settled in favor of a canted Néel order, the seemingly disordered intermediate phase arising around J₂=1/8 is still poorly understood, with conventional numerical methods giving ambiguous and conflicting results. To bring new insight to this problem, we apply hierarchical mean-field theory (HMFT). HMFT has been successfully applied to a number of related frustrated magnetic systems, most relevantly the square lattice Heisenberg antiferromagnet. Inspired by analysis of HMFT solutions on a number of clusters preserving and breaking specific symmetries of the TLHA, we develop a parameter indicating plaquette-crystal order in the intermediate phase. To better understand this phase, we also examine its stability as the ZZ interactions are tuned to zero (giving the XY model) and in the presence of third-nearest neighbor interactions.