Nematic quantum phases in the bilayer honeycomb antiferromagnet

The spin-$1/2$ Heisenberg antiferromagnet on the honeycomb bilayer lattice is shown to display a rich variety of semiclassical and genuinely quantum phases, controlled by the interplay between intralayer frustration and interlayer exchange. Employing a complementary set of techniques, comprising spin rotationally invariant Schwinger boson mean-field theory, bond operators, and series expansions, we unveil the quantum phase diagram, analyzing low-energy excitations and order parameters. By virtue of Schwinger bosons we scan the complete range of exchange parameters, covering both long-range-ordered and quantum disordered ground states, and reveal the existence of an extended, frustration-induced lattice nematic phase in a range of intermediate exchange unexplored so far.

Figure 1

Schematic representation of the model. The sites (green spheres) in each unit cell are labeled from 1 to 4. Thick vertical blue lines indicate $J_{\perp }$ interlayer couplings, whereas thin black and red lines indicate $J_1$ and $J_2$ first- and second-nearest neighbors, respectively.

Figure 2

(a) The different colored regions identify the phases of model (1) in the $J_2\text{−}{J}_{\perp }$ plane (in units of $J_1$) determined by SBMFT. The blue and red lines represent the border of the IDP phase predicted by SE and BO, respectively. (b) Zoom of the phase diagram where two paths along $J_{\perp }$ for $J_2=0.3$ and $J_2=0.38$ are indicated with red dashed lines. (c) and (d) The evolution of the gap (connected red circles) and the $Z_3$ directional symmetry-breaking order parameter $\rho$ (connected black squares) along the mentioned paths.

Figure 3

Contour plot corresponding to the bond-operator boson dispersion close to condensation for (a) $J_2/J_1=0.1$, (b) $J_2/J_1=0.4$, and (c) $J_2/J_1=0.6$. Red dashed lines correspond to curves in the $\vec{k}$ space determining the classical manifold of spiral ground states.