We perform a density-matrix renormalization group (DMRG) study of the S=1/2 Heisenberg antiferromagnet on the kagome lattice to identify the conjectured spin liquid ground state. Exploiting SU(2) spin symmetry, which allows us to keep up to 16,000 DMRG states, we consider cylinders with circumferences up to 17 lattice spacings and find a spin liquid ground state with an estimated per site energy of -0.4386(5), a spin gap of 0.13(1), very short-range decay in spin, dimer and chiral correlation functions, and finite topological entanglement γ consistent with γ=log(2)2, ruling out gapless, chiral, or nontopological spin liquids in favor of a topological spin liquid of quantum dimension 2, with strong evidence for a gapped topological Z(2) spin liquid.

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 ≈ 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 √ 3 × √ 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.

In magnetically ordered systems, the breaking of SU(2) symmetry in the thermodynamic limit is associated with the appearance of a special type of low-lying excitations in finite-size energy spectra, the so-called tower of states (TOS). In the present work, we numerically demonstrate that there is a correspondence between the SU(2) tower of states and the lower part of the ground-state entanglement spectrum (ES). Using state-of-the-art density matrix renormalization group (DMRG) calculations, we examine the ES of the 2D antiferromagnetic J 1 -J 2 Heisenberg model on both the triangular and kagome lattice. At large ferromagnetic J 2 , the model exhibits a magnetically ordered ground state. Correspondingly, its ES contains a family of low-lying levels that are reminiscent of the energy tower of states. Their behavior (level counting, finite-size scaling in the thermodynamic limit) sharply reflects TOS features, and is characterized in terms of an effective entanglement Hamiltonian that we provide. At large system sizes, TOS levels are divided from the rest by an entanglement gap. Our analysis suggests that (TOS) entanglement spectroscopy provides an alternative tool for detecting and characterizing SU(2)-broken phases using DMRG.

We perform a density-matrix renormalization group (DMRG) study of the S = 1 2 Heisenberg antiferromagnet on the kagome lattice to identify the conjectured spin liquid ground state. Exploiting SU(2) spin symmetry, which allows us to keep up to 16 000 DMRG states, we consider cylinders with circumferences up to 17 lattice spacings and find a spin liquid ground state with an estimated per site energy of −0.4386(5), a spin gap of 0.13(1), very short-range decay in spin, dimer and chiral correlation functions and finite topological entanglement γ consistent with γ = log 2 2, ruling out gapless, chiral or non-topological spin liquids in favor of a topological spin liquid of quantum dimension 2, with strong evidence for a gapped topological Z2 spin liquid.

We study an SU (2) symmetric spin-3/2 model on the z = 3 Bethe lattice using the infinite Time Evolving Block Decimation (iTEBD) method. This model is shown to exhibit a rich phase diagram. We compute the expectation values of several order parameters which allow us to identify a ferromagnetic, a ferrimagnetic, a anti-ferromagnetic as well as a dimerized phase. We calculate the entanglement spectra from which we conclude the existence of a symmetry protected topological phase that is characterized by S = 1/2 edge spins. Details of the iTEBD algorithm used for the simulations are included.