Phase diagram and chirality of the spin-1/2 J1-J2 Heisenberg model on the kagome lattice

We studied the spin-1/2 Heisenberg model on the kagome lattice with nearest (J1) and next-nearest neighbor (J2) interactions by means of the density matrix renormalization group. We set J1 as antiferromagnetic coupling (J1 \textgreater\ 0), and J2 can be either ferromagnetic (J2 \textless\ 0) or antiferromagnetic (J2 \textgreater\ 0). By analyzing the spin-spin correlation function and the bond energy, we find a valence-bond crystal phase for J2 \textless\ -0.1 and a magnetically ordered phase for J2 \textgreater\ 0.2. In the intermediate paramagnetic phase, we investigate the evolution of spin and singlet gaps, topological entanglement entropy, dimer and chirality correlations as a function of the parameter J2. In particular, we investigate the local p6 chiral order parameter proposed recently by measuring the dimer-dimer correlation functions to study the possible reflection symmetry breaking in this spin liquid candidate.