Transverse Magnetic Susceptibility of a Frustrated Spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ Heisenberg Antiferromagnet on a Bilayer Honeycomb Lattice

TL;DR

This study uses the coupled cluster method to accurately map the phase boundary of a frustrated bilayer honeycomb antiferromagnet, revealing a transition from magnetic order to a gapped paramagnetic phase with reentrant behavior.

Contribution

The paper provides the first high-order CCM calculation of the transverse susceptibility to determine the quantum phase boundary in a frustrated bilayer honeycomb model.

Findings

Phase boundary accurately mapped in the $$-$$ plane.

Transition from Nel order to a gapped paramagnetic phase.

Reentrant behavior observed along the phase boundary.

Abstract

We use the coupled cluster method (CCM) to study a frustrated spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ Heisenberg antiferromagnet on a bilayer honeycomb lattice with $AA$ stacking. Both nearest-neighbor (NN) and frustrating next-nearest-neighbor antiferromagnetic (AFM) exchange interactions are present in each layer, with respective exchange coupling constants $J_{1}>0$ and $J_{2} \equiv \kappa J_{1} > 0$. The two layers are coupled with NN AFM exchanges with coupling strength $J_{1}^{\perp}\equiv \delta J_{1}>0$. We calculate to high orders of approximation within the CCM the zero-field transverse magnetic susceptibility $\chi$ in the N\'eel phase. We thus obtain an accurate estimate of the full boundary of the N\'eel phase in the $\kappa\delta$ plane for the zero-temperature quantum phase diagram. We demonstrate explicitly that the phase boundary derived from $\chi$ is fully consistent with that obtained from the vanishing of the N\'eel magnetic order parameter. We thus conclude that at all points along the N\'eel phase boundary quasiclassical magnetic order gives way to a nonclassical paramagnetic phase with a nonzero energy gap. The N\'eel phase boundary exhibits a marked reentrant behavior, which we discuss in detail.