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We perform an extensive density matrix renormalization group (DMRG) study ofthe ground-state phase diagram of the spin-1/2 J_1-J_2 Heisenberg model on thekagome lattice. We focus on the region of the phase diagram around the kagomeHeisenberg antiferromagnet, i.e., at J_2=0. We investigate the static spinstructure factor, the magnetic correlation lengths, and the spin gaps. Ourresults are consistent with the absence of magnetic order in a narrow regionaround J_2\approx 0, although strong finite-size effects do not allow us toaccurately determine the phase boundaries. This result is in agreement with thepresence of an extended spin-liquid region, as it has been proposed recently.Outside the disordered region, we find that for ferromagnetic andantiferromagnetic J_2 the ground state displays signatures of the magneticorder of the \sqrt{3}\times\sqrt{3} and the q=0 type, respectively. Finally, wefocus on the structure of the entanglement spectrum (ES) in the q=0 orderedphase. We discuss the importance of the choice of the bipartition on thefinite-size structure of the ES.

Phase diagram of the J1-J2 Heisenberg model on the kagome lattice