Competing Paramagnetic Phases in the Maple-Leaf Heisenberg Antiferromagnet

TL;DR

This paper maps out a complex phase diagram of the spin-1/2 Heisenberg antiferromagnet on the maple-leaf lattice, revealing multiple competing magnetic and spin liquid phases with potential for exotic quantum states.

Contribution

It identifies and characterizes several novel magnetic and spin liquid phases in the maple-leaf lattice, including a candidate $ ext{Z}_2$ spin liquid, using exact diagonalization and wave-function analysis.

Findings

Discovery of a star-shaped valence bond solid state near the 120° phase

Identification of an exact dimer product state close to Nél order

Evidence for a gapped $ ext{Z}_2$ spin liquid in a specific parameter regime

Abstract

We establish a remarkably rich ground state phase diagram in the maple-leaf lattice spin-$1/2$ Heisenberg antiferromagnet as a function of the three symmetry-inequivalent nearest-neighbor bonds using exact diagonalization and tower-of-states analysis on clusters up to $N=36$ sites. Besides a hexagonal plaquette state, a star-shaped valence bond solid state is discovered in close vicinity to the (canted) $120^\circ$ magnetic phase, strongly reminiscent of a de-confined critical point or Dirac spin liquid scenario on the triangular lattice antiferromagnets. Moreover, an exact dimer product-state is observed next to a collinear N\'eel-state, similar to the Shastry-Sutherland model. All identified phases compete in a parameter regime close to the isotropic point, providing a promising region for spin liquids to emerge. By analyzing Gutzwiller-projected wave-functions we identify a sliver of parameter regime where a gapped $\mathbb{Z}_{2}$ spin liquid Ansatz is in astonishing agreement with the exact $N=36$ ground state. This rich competition of paramagnetic phases demonstrates that the maple-leaf antiferromagnet is a promising platform for exotic states of matter and quantum critical phenomena.