For a class of frustrated spin lattices including the kagomé lattice we construct exact eigenstates consisting of several independent, localized one-magnon states and argue that they are ground states for high magnetic fields. If the maximal number of local magnons scales with the number of spins in the system, which is the case for the kagomé lattice, the effect persists in the thermodynamic limit and gives rise to a macroscopic jump in the zero-temperature magnetization curve just below the saturation field. The effect decreases with increasing spin quantum number and vanishes in the classical limit. Thus it is a true macroscopic quantum effect.In frustrated quantum spin lattices the competition of quantum and frustration effects promises rich physics. A reliable description of such systems often constitutes a challenge for theory. A famous example is the kagomé lattice antiferromagnet. In spite of extensive studies during the last decade its ground state properties are not fully understood yet. Classically it has infinite continuous degeneracies. In the quantum case (s=1/2), the system is likely to be a spin liquid with a gap for magnetic excitations and a huge number of singlet states below the first triplet state (see [1,2,3] and references therein).In this Letter we will focus on the zero-temperature magnetic behavior of highly frustrated lattices, in particular for high magnetic fields. One aspect is given by the observation of nontrivial magnetic plateaus in frustrated two dimensional (2D) quantum antiferromagnets like SrCu 2 (BO 3 ) [4,5], which has stimulated theoretical interest (see e.g. [6]). Also the kagomé lattice has a plateau at one third (m = 1/3) of the saturation magnetization [7,8]. Since this plateau can be found also in the Ising model and in the classical Heisenberg model with additional thermal fluctuations [9] it can be considered to be of classical origin. However, the structure of the ground state in the classical model is highly non-trivial at m = 1/3 [10] and has not been clarified yet for the quantum model.Another aspect is given by unusual jumps seen in magnetization curves. Such jumps can arise for different reasons. One possibility is a first-order transition between different ground states like the spin flop transition in classical magnets or in strongly anisotropic quantum chains [11]. Here we discuss another possibility, namely a macroscopically large degeneracy in the exact ground states of the full quantum system for a certain value of the applied field. We argue that this is a general phenomenon in highly frustrated systems. This is remarkable in so far as one can exactly write down ground states at a finite density of magnons in a strongly correlated system which is neither integrable, nor has any apparent non-trivial conservation laws. Such jumps represent a genuine macroscopic quantum effect which is also of possible experimental relevance since it occurs in many wellknown models like the kagomé lattice. This jump occurs just below saturation and should be observable in...

Inelastic neutron scattering, susceptibility, and high-field magnetization identify LiCuVO4 as a nearest-neighbour ferromagnetic, next-nearest-neighbour frustrated, quasi-onedimensional helimagnet, which is largely influenced by quantum fluctuations. Complementary band structure calculations provide a microscopic model with the correct sign and magnitude of the major exchange integrals.

Using the coupled cluster method for high orders of approximation and complementary exact diagonalization studies we investigate the ground state properties of the spin-1/2 J 1 -J 2 frustrated Heisenberg antiferromagnet on the square lattice. We have calculated the ground state energy, the magnetic order parameter, the spin stiffness, and several generalized susceptibilities to probe magnetically disordered quantum valence-bond phases. We have found that the quantum critical points for both the Néel and collinear orders are J 2 c1 Ϸ͑0.44Ϯ 0.01͒J 1 and J 2 c2 Ϸ͑0.59Ϯ 0.01͒J 1 , respectively, which are in good agreement with the results obtained by other approximations. In contrast to the recent study by ͓Sirker et al. Phys. Rev. B 73, 184420 ͑2006͔͒, our data do not provide evidence for the transition from the Néel to the valence-bond solid state to be first order. Moreover, our results are in favor of the deconfinement scenario for that phase transition. We also discuss the nature of the magnetically disordered quantum phase.

In this article we focus on the ground state and the low-lying excitations of the s = 1/2 Heisenberg antiferromagnet (HAFM) on the 11 two-dimensional (2D) uniform Archimedean lattices.Although we know from the Mermin-Wagner theorem that thermal fluctuations are strong enough to destroy magnetic long-range order (LRO) for Heisenberg spin systems at any finite temperature in one and two dimensions, the role of quantum fluctuations is less understood. While the ground state of the one-dimensional (1D) quantum HAFM is not long-range ordered, the quantum HAFM e.g. on the 2D square and triangular lattices exhibits semiclassical Néel like LRO. However, in two dimensions there are many other lattices with different coordination numbers and topologies, and there is no general statement concerning zero-temperature Néel-like LRO. Recent experimental results on CaV 4 O 9 and SrCu 2 (BO 3 ) 2 demonstrate the possibility of non-Néel ordered ground states and signal that the s = 1/2 HAFM on 2D lattices with appropriate topology may have a ground state without semiclassical LRO.Based on extensive large-scale exact diagonalization studies of the ground state and the low-lying excitations for the spin-1/2 HAFM on the Archimedean lattices we compare and discuss the ground-state features of all 11 lattices. 2 Richter, Schulenburg, and HoneckerIn this manner we obtain some insight in the influence of lattice topology on magnetic ordering of quantum antiferromagnets in two dimensions. From our results we conclude that the ground state of the spin-1/2 HAFM on most of the Archimedean lattices (in particular the four bipartite ones) turns out to be semi-classically Néel-like ordered. However, we find that the interplay of competition of bonds (geometric frustration and non-equivalent nearest neighbor bonds) and quantum fluctuations gives rise to a quantum paramagnetic ground state without semi-classical LRO for two lattices. The first one is the famous kagomé lattice, for which this statement is well-known by numerous studies during the last decade. Remarkably, we find one additional lattice among the 11 uniform Archimedean lattices, the so-called star lattice, with a quantum paramagnetic ground state. For both these Archimedean lattices the ground state is highly degenerate in the classical limit s → ∞, although notably their quantum ground states are fundamentally different.Furthermore, we present numerical results for the magnetization curve of the HAFM on all 11 Archimedean lattices. The magnetization process is discussed in some detail for the square, triangular and kagomé lattices. One focus are plateaus appearing in the magnetization curve due to quantum fluctuations and geometric frustration. In particular, the kagomé lattice exhibits a rich spectrum of magnetization plateaus. Another focus are magnetization jumps arising on the kagomé and the star lattice just below the saturation field. These magnetization jumps may be understood analytically by using independent local magnon excitations.Some related s = 1/2 models are also dis...

We study the zero-temperature phase diagram and the low-lying excitations of a square-lattice spinhalf Heisenberg antiferromagnet with two types of regularly distributed nearest-neighbour exchange bonds (J > 0 (antiferromagnetic) and −∞ < J ′ < ∞) using the coupled cluster method (CCM) for high orders of approximation (up to LSUB8). We use a Néel model state as well as a helical model state as a starting point for the CCM calculations. We find a second-order transition from a phase with Néel order to a finite-gap quantum disordered phase for sufficiently large antiferromagnetic exchange constants J ′ > 0. For frustrating ferromagnetic couplings J ′ < 0 we find indications that quantum fluctuations favour a first-order phase transition from the Néel order to a quantum helical state, by contrast with the corresponding second-order transition in the corresponding classical model. The results are compared to those of exact diagonalizations of finite systems (up to 32 sites) and those of spin-wave and variational calculations. The CCM results agree well with the exact diagonalization data over the whole range of the parameters. The special case of J ′ = 0, which is equivalent to the honeycomb lattice, is treated more closely.