We present results for a complementary analysis of the frustrated planar J 1 -J 2 -J 3 spin-1/2 quantum antiferromagnet (AFM). Using dynamical functional renormalization group, high-order-coupled cluster calculations, and series expansion based on the flow equation method, we have calculated generalized momentum-resolved susceptibilities, the ground-state energy, the magnetic-order parameter, and the elementary excitation gap. From these, we determine a quantum phase diagram that shows a large window of a quantum paramagnetic (QP) phase situated among the Néel, spiral, and collinear states, which are present already in the classical J 1 -J 2 -J 3 AFM. Our findings are consistent with substantial plaquette correlations in the QP phase. The extent of the QP region is found to be in satisfying agreement between the three different approaches we have employed.

We use a combination of analytical and numerical techniques to study the phase diagram of the frustrated Heisenberg model on the bilayer honeycomb lattice. Using the Schwinger boson description of the spin operators followed by a mean field decoupling, the magnetic phase diagram is studied as a function of the frustration coupling J2 and the interlayer coupling J ⊥ .The presence of both magnetically ordered and disordered phases is investigated by means of the evaluation of ground-state energy, spin gap, local magnetization and spin-spin correlations. We observe a phase with a spin gap and short range Néel correlations that survives for non-zero next-nearest-neighbor interaction and interlayer coupling. Furthermore, we detect signatures of a reentrant behavior in the melting of Néel phase and symmetry restoring when the system undergoes a transition from an on-layer nematic valence bond crystal phase to an interlayer valence bond crystal phase. We complement our work with exact diagonalization on small clusters and dimerseries expansion calculations, together with a linear spin wave approach to study the phase diagram as a function of the spin S, the frustration and the interlayer couplings.

We show that spin-S chains with SU(2)-symmetric, ferromagnetic nearest-neighbor and frustrating antiferromagnetic next-nearest-neighbor exchange interactions exhibit metamagnetic behavior under the influence of an external magnetic field for small S, in the form of a first-order transition to the fully polarized state. The corresponding magnetization jump increases gradually starting from an S-dependent critical value of exchange couplings and takes a maximum in the vicinity of a ferromagnetic Lifshitz point. The metamagnetism results from resonances in the dilute magnon gas caused by an interplay between quantum fluctuations and frustration.

We study the magnetism of a frustrated four-leg spin-1/2 ladder with transverse periodic boundary conditions: the frustrated four-spin tube (FFST). Using a combination of series expansion (SE), based on the continuous unitary transformation method and density-matrix renormalization group (DMRG) we analyze the ground-state, the one-, and the two-particle excitations in the regime of strong rung-coupling. We find several marked differences of the FFST with respect to standard two-leg ladders. First we show that frustration destabilizes the spin-gap phase of the FFST which is adiabatically connected to the limit of decoupled rung singlets, leading to a first order quantum phase transition at finite inter-rung coupling. Second, we show that apart from the well-know triplon branch of spin-ladders, the FFST sustains additional elementary excitations, including a singlon, and additional triplons. Finally we find, that in the two-particle sector the FFST exhibits collective (anti)bound states similar to two-leg ladders, however with a different ordering of the spin-quantum numbers. We show that frustration has significant impact on the FFST leading to a flattening of the ground-state energy landscape, a mass-enhancement of the excitations, and to a relative enhancement of the (anti)binding strength. Where possible we use DMRG to benchmark the findings from our SE calculations, showing excellent agreement.