Abstract
We perform an extensive density-matrix renormalization-group study of the ground-state phase diagram of the spin-1/2 J(1)-J(2) Heisenberg model on the kagome lattice. We focus on the region of the phase diagram around the kagome Heisenberg antiferromagnet, i.e., at J(2) = 0. We investigate the static spin structure factor, the magnetic correlation lengths, and the spin gaps. Our results are consistent with the absence of magnetic order in a narrow region around J(2) approximate to 0, although strong finite-size effects do not allow us to accurately determine the phase boundaries. This result is in agreement with the presence of an extended spin-liquid region, as it has been proposed recently. Outside the disordered region, we find that for ferromagnetic and antiferromagnetic J(2), the ground state displays signatures of the magnetic order of the root 3 x root 3 and the q = 0 type, respectively. Finally, we focus on the structure of the entanglement spectrum (ES) in the q = 0 ordered phase. We discuss the importance of the choice of the bipartition on the finite-size structure of the ES.