The spin-half Heisenberg antiferromagnet on two Archimedian lattices: From the bounce lattice to the maple-leaf lattice and beyond

TL;DR

This study explores the ground state and magnetic properties of the Heisenberg antiferromagnet on two Archimedean lattices, revealing a transition from magnetic order to a quantum dimer state as frustration increases.

Contribution

It provides a detailed analysis of the phase diagram of the $J$-$J'$ model on Archimedean lattices, identifying a first-order transition to an orthogonal-dimer singlet state and characterizing magnetization plateaus.

Findings

Magnetic long-range order persists over a wide parameter range.

A first-order transition occurs at $J'_c \\approx 1.45 J$ to a dimerized state.

Magnetization plateaus at 1/3 and 2/3 emerge at large $J'/J$.

Abstract

We investigate the ground state of the two-dimensional Heisenberg antiferromagnet on two Archimedean lattices, namely, the maple-leaf and bounce lattices as well as a generalized $J$-$J'$ model interpolating between both systems by varying $J'/J$ from $J'/J=0$ (bounce limit) to $J'/J=1$ (maple-leaf limit) and beyond. We use the coupled cluster method to high orders of approximation and also exact diagonalization of finite-sized lattices to discuss the ground-state magnetic long-range order based on data for the ground-state energy, the magnetic order parameter, the spin-spin correlation functions as well as the pitch angle between neighboring spins. Our results indicate that the "pure" bounce ($J'/J=0$) and maple-leaf ($J'/J=1$) Heisenberg antiferromagnets are magnetically ordered, however, with a sublattice magnetization drastically reduced by frustration and quantum fluctuations. We found that magnetic long-range order is present in a wide parameter range $0 \le J'/J \lesssim J'_c/J $ and that the magnetic order parameter varies only weakly with $J'/J$. At $J'_c \approx 1.45 J$ a direct first-order transition to a quantum orthogonal-dimer singlet ground state without magnetic long-range order takes place. The orthogonal-dimer state is the exact ground state in this large-$J'$ regime, and so our model has similarities to the Shastry-Sutherland model. Finally, we use the exact diagonalization to investigate the magnetization curve. We a find a 1/3 magnetization plateau for $J'/J \gtrsim 1.07$ and another one at 2/3 of saturation emerging only at large $J'/J \gtrsim 3$.