Valence-bond crystalline order in the $s=1/2$ $J_1$--$J_2$ model on the honeycomb lattice

Abstract

Using the coupled cluster method we study the phase diagram of the spin-1/2 Heisenberg antiferromagnet on a honeycomb lattice with nearest-neighbor exchange coupling $J_1>0$ and frustrating next-nearest-neighbor coupling $J_2\equiv x{J}_1>0$. In the range $0<x<1$ we find four phases exhibiting respectively Néel, 6-spin plaquette, staggered dimer, and Néel-II orderings, with quantum critical points at $x_{c_1}\approx 0.207(3),x_{c_2}\approx 0.385(10)$, and $x_{c_3}\approx 0.65(5)$. The transitions at $x_{c_1}$ and $x_{c_3}$ appear to be continuous (and hence deconfined) ones, while that at $x_{c_2}$ appears to be a direct first-order one.

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