Phase diagram of the spin-12J1-J2Heisenberg model on a honeycomb lattice

Abstract

We use the density matrix renormalization group (DMRG) algorithm to study the phase diagram of the spin-$\frac{1}{2}$ Heisenberg model on a honeycomb lattice with first (${J}_{1}$) and second (${J}_{2}$) neighbor antiferromagnetic interactions, where a ${Z}_{2}$ spin liquid region has been proposed. By implementing SU(2) symmetry in the DMRG code, we are able to obtain accurate results for long cylinders with a width slightly over 15 lattice spacings and a torus up to the size $N=2\ifmmode\times\else\texttimes\fi{}6\ifmmode\times\else\texttimes\fi{}6$. With increasing ${J}_{2}$, we find a N\'eel phase with a vanishing spin gap and a plaquette valence-bond (PVB) phase with a nonzero spin gap. By extrapolating the square of the staggered magnetic moment ${m}_{s}^{2}$ on finite-size cylinders to the thermodynamic limit, we find the N\'eel order vanishing at ${J}_{2}/{J}_{1}\ensuremath{\simeq}0.22$. For $0.25<{J}_{2}/{J}_{1}\ensuremath{\le}0.35$, we find a possible PVB order, which shows a fast growing PVB decay length with increasing system width. For $0.22<{J}_{2}/{J}_{1}<0.25$, both spin and dimer orders vanish in the thermodynamic limit, which is consistent with a possible spin liquid phase. We present calculations of the topological entanglement entropy, compare the DMRG results with the variational Monte Carlo, and discuss possible scenarios in the thermodynamic limit for this region.