We introduce a computable estimator of block entanglement entropy for many-body spin systems admitting total singlet ground states. Building on a simple geometrical interpretation of entanglement entropy of the so-called valence bond states, this estimator is defined as the average number of common singlets to two subsystems of spins. We show that our estimator possesses the characteristic scaling properties of the block entanglement entropy in critical and noncritical one-dimensional Heisenberg systems. We invoke this new measure to examine entanglement scaling in the two-dimensional Heisenberg model on a square lattice revealing an "area law" for the gapped phase and a logarithmic correction to this law in the gapless phase.

We discuss the ground state, the low-lying excitations as well as high-field thermodynamics of the Heisenberg antiferromagnet on the two-dimensional square-kagomé lattice. This magnetic system belongs to the class of highly frustrated spin systems with an infinite non-trivial degeneracy of the classical ground state as it is also known for the Heisenberg antiferromagnet on the kagomé and on the star lattice. The quantum ground state of the spin-half system is a quantum paramagnet with a finite spin gap and with a large number of non-magnetic excitations within this gap. We also discuss the magnetization versus field curve that shows a plateaux as well as a macroscopic magnetization jump to saturation due to independent localized magnon states. These localized states are highly degenerate and lead to interesting features in the low-temperature thermodynamics at high magnetic fields such as an additional low-temperature peak in the specific heat and an enhanced magnetocaloric effect.

We present an analysis of the entanglement characteristics in the Majumdar-Ghosh (MG) or $J_{1}$-$J_{2}$ Heisenberg model. For a system consisting of up to 28 spins, there is a deviation from the scaling behaviour of the entanglement entropy characterizing the unfrustrated Heisenberg chain as soon as $J_{2} >0.25$. This feature can be used as an indicator of the dimer phase transition that occurs at $J_{2} = J_{2}^{*} \approx 0.2411 J_{1}$. Additionally, we also consider entanglement at the MG point $J_{2}=0.5 J_{1}$.Comment: 7 figure

A linear spin-wave approach, a variational method and exact diagonlization are used to investigate the magnetic long-range order (LRO) of the spin-1 2 Heisenberg antiferromagnet on a two-dimensional 1/7-depleted triangular (maple leaf) lattice consisting of triangles and hexagons only. This lattice has z = 5 nearest neighbors and its coordination number z is therefore between those of the triangular (z = 6) and the kagomé (z = 4) lattices. Calculating spin-spin correlations, sublattice magnetization, spin stiffness, spin-wave velocity and spin gap we find that the classical 6-sublattice LRO is strongly renormalized by quantum fluctuations, however, remains stable also in the quantum model.