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.

We study the low-temperature thermodynamic properties of a number of frustrated quantum antiferromagnets which support localized magnon states in the vicinity of the saturation field. For this purpose we use 1) a mapping of the low-energy degrees of freedom of spin systems onto the hard-core object lattice gases and 2) an exact diagonalization of finite spin systems of up to N = 30 sites. The considered spin systems exhibit universal behavior which is determined by a specific hard-core object lattice gas representing the independent localized magnon states. We test the lattice gas description by comparing its predictions with the numerical results for low-lying energy states of finite spin systems. For all frustrated spin systems considered we find a strong variation of the low-temperature specific heat passing the saturation field and a maximum in the isothermal entropy at saturation field resulting in an enhanced magnetocaloric effect. [7,8]). These ground states consist of independent (i.e. isolated) localized magnons in a ferromagnetic environment. The localized magnon states were used to predict a ground-state magnetization jump at the saturation field [4-6], a magnetic field induced spin-Peierls instability [9,10], and a residual ground-state entropy at the saturation field [3,8,[11][12][13]. Moreover, in Refs. [8,12,13] the concept of localized magnons was used for a detailed analysis of the low-temperature magnetothermodynamics in the vicinity of the saturation field for two representative systems, the sawtooth chain (or ∆-chain) and the kagomé lattice. In particular, the authors of these papers mapped the low-energy degrees of freedom of the sawtooth chain (the kagomé lattice) to the hard-dimer gas on a one-dimensional lattice (the hard-hexagon gas on a triangular lattice) and used the results for the classical lattice gases to discuss the properties of the spin systems. They also 1

Using the coupled-cluster method (CCM) and the rotation-invariant Green's function method (RGM), we study the influence of the interlayer coupling J ⊥ on the magnetic ordering in the ground state of the spin-1/2 J1-J2 frustrated Heisenberg antiferromagnet (J1-J2 model) on the stacked square lattice. In agreement with known results for the J1-J2 model on the strictly two-dimensional square lattice (J ⊥ = 0) we find that the phases with magnetic long-range order at small J2 < Jc 1 and large J2 > Jc 2 are separated by a magnetically disordered (quantum paramagnetic) ground-state phase. Increasing the interlayer coupling J ⊥ > 0 the parameter region of this phase decreases, and, finally, the quantum paramagnetic phase disappears for quite small J ⊥ ∼ 0.2 − 0.3J1.The properties of the frustrated spin-1/2 Heisenberg antiferromagnet (HAFM) with nearest-neighbor J 1 and competing next-nearest-neighbor J 2 coupling (J 1 -J 2 model) on the square lattice have attracted a great deal of interest during the last fifteen years (see, e.g., Refs. 1-12 and references therein). The recent synthesis of layered magnetic materials 13,14 which can be described by the J 1 -J 2 model has stimulated a renewed interest in this model. It is well-accepted that the model exhibits two magnetically long-range ordered phases at small and at large J 2 separated by an intermediate quantum paramagnetic phase without magnetic long-range order (LRO) in the parameter region J c1 < J 2 < J c2 , where J c1 ≈ 0.4 and J c2 ≈ 0.6. The ground state (GS) at low J 2 < J c1 exhibits semi-classical Néel magnetic LRO with the magnetic wave vector Q 0 = (π, π). The GS at large J 2 > J c2 shows so-called collinear magnetic LRO with the magnetic wave vectors Q 1 = (π, 0) or Q 2 = (0, π). These two collinear states are characterized by a parallel spin orientation of nearest neighbors in vertical (horizontal) direction and an antiparallel spin orientation of nearest neighbors in horizontal (vertical) direction. The properties of the intermediate quantum paramagnetic phase are still under discussion, however, a valence-bond crystal phase seems to be most favorable. 2-4,8,9The properties of quantum magnets strongly depend on the dimensionality.15 Though the tendency to order is more pronounced in three-dimensional (3d) systems than in low-dimensional ones, a magnetically disordered phase can also be observed in frustrated 3d systems such as the HAFM on the pyrochlore lattice 16 or on the stacked kagomé lattice.17 On the other hand, recently it has been found that the 3d J 1 -J 2 model on the body-centered cubic lattice does not have an intermediate quantum paramagnetic phase.18,19 Moreover, in experimental realizations of the J 1 -J 2 model the magnetic couplings are expected to be not strictly 2d, but a finite interlayer coupling J ⊥ is present. For example, recently Rosner et al.14 have found J ⊥ /J 1 ∼ 0.07 for Li 2 VOSiO 4 , a material which can be described by a square lattice J 1 -J 2 model with large J 2 . 13,14This motivates us to consider an extension of the...

On a large class of lattices (such as the sawtooth chain, the kagome and the pyrochlore lattices) the quantum Heisenberg and the repulsive Hubbard models may host a completely dispersionless (flat) energy band in the single-particle spectrum. The flat-band states can be viewed as completely localized within a finite volume (trap) of the lattice and allow for construction of many-particle states, roughly speaking, by occupying the traps with particles. If the flat band happens to be the lowest-energy one the manifold of such many-body states will often determine the ground-state and low-temperature physics of the models at hand even in the presence of strong interactions. The localized April 14, 2015 0:38 WSPC/INSTRUCTION FILE de˙ri˙ma˙revised 2 O. Derzhko, J. Richter, M. Maksymenko nature of these many-body states makes possible the mapping of this subset of eigenstates onto a corresponding classical hard-core system. As a result, the ground-state and lowtemperature properties of the strongly correlated flat-band systems can be analyzed in detail using concepts and tools of classical statistical mechanics (e.g., classical lattice-gas approach or percolation approach), in contrast to more challenging quantum many-body techniques usually necessary to examine strongly correlated quantum systems.In this review we recapitulate the basic features of the flat-band spin systems and briefly summarize earlier studies in the field. Main emphasis is made on recent developments which include results for both spin and electron flat-band models. In particular, for flat-band spin systems we highlight field-driven phase transitions for frustrated quantum Heisenberg antiferromagnets at low temperatures, chiral flat-band states, as well as the effect of a slight dispersion of a previously strictly flat band due to nonideal lattice geometry. For electronic systems, we discuss the universal low-temperature behavior of several flat-band Hubbard models, the emergence of ground-state ferromagnetism in the square-lattice Tasaki-Hubbard model and the related Pauli-correlated percolation problem, as well as the dispersion-driven ground-state ferromagnetism in flat-band Hubbard systems. Closely related studies and possible experimental realizations of the flat-band physics are also described briefly.a Magnetic interactions are frustrated, if a spin cannot arrange its orientation such that it profits from the interaction with its neighbors as, for instance, in the case of antiferromagnetic interactions on the triangular lattice. For a more in depth discussion we refer to Refs. 6, 7. April 14, 2015 0:38 WSPC/INSTRUCTION FILE de˙ri˙ma˙revised Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons 3ometry of the lattice. The very existence of localized magnons as the lowest-energy one-particle states opens an interesting perspective to construct and fully characterize many-magnon ground states of the considered frustrated quantum Heisenberg antiferromagnets. Moreover, the set of relevant low-energy many-magn...