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.

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

1 J 2 J 3 J FIG. 1: The dimer-plaquette chain which hosts three localized magnons at fat bonds (top) and the auxiliary lattice used for the calculation of the ground-state degeneracy at saturation (bottom). The localized magnons are eigenstates for large enough vertical bonds J3 ≥ J c 3 (J1, J2) 16 .

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...

The purpose of the present paper is two-fold. On the one hand, we review some recent studies on the low-temperature strong-field thermodynamic properties of frustrated quantum spin antiferromagnets which admit the so-called localized-magnon eigenstates. One the other hand, we provide some complementary new results. We focus on the linear independence of the localized-magnon states, the estimation of their degeneracy with the help of auxiliary classical lattice-gas models and the analysis of the contribution of these states to thermodynamics. PACS: 75.10.Jm Quantized spin models; 75.45.+j Macroscopic quantum phenomena in magnetic systems; 75.50.Ee Antiferromagnetics.

We clarify the existence of several magnetization plateaus for the kagome S = 1 2 antiferromagnetic Heisenberg model in a magnetic field. Using approximate or exact localized magnon eigenstates, we are able to describe in a similar manner the plateau states that occur for magnetization per site m = 1 3 , 5 9 , and 7 9 of the saturation value. These results are confirmed using large-scale exact diagonalization on lattices up to 63 sites.

For a class of frustrated antiferromagnetic spin lattices (in particular, the square-kagomé and kagomé lattices) we discuss the impact of recently discovered exact eigenstates on the stability of the lattice against distortions. These eigenstates consist of independent localized magnons embedded in a ferromagnetic environment and become ground states in high magnetic fields. For appropriate lattice distortions fitting to the structure of the localized magnons the lowering of magnetic energy can be calculated exactly and is proportional to the displacement of atoms leading to a spin-Peierls lattice instability. Since these localized states are present only for high magnetic fields, this instability might be driven by magnetic-field. The hysteresis of the spin-Peierls transition is also discussed.

We consider the repulsive Hubbard model on three highly frustrated one-dimensional latticessawtooth chain and two kagomé chains -with completely dispersionless (flat) lowest single-electron bands. We construct the complete manifold of exact many-electron ground states at low electron fillings and calculate the degeneracy of these states. As a result, we obtain closed-form expressions for low-temperature thermodynamic quantities around a particular value of the chemical potential µ0. We discuss specific features of thermodynamic quantities of these ground-state ensembles such as residual entropy, an extra low-temperature peak in the specific heat, and the existence of ferromagnetism and paramagnetism. We confirm our analytical results by comparison with exact diagonalization data for finite systems.