Abstract. Motivated by recent experiments on thin films of the ferromagnetic insulator yttrium-iron garnet (YIG), we have developed an efficient microscopic approach to calculate the spin-wave spectra of these systems. We model the experimentally relevant magnon band of YIG using an effective quantum Heisenberg model on a cubic lattice with ferromagnetic nearest neighbour exchange and long-range dipole-dipole interactions. After a bosonization of the spin degrees of freedom via a Holstein-Primakoff transformation and a truncation at quadratic order in the bosons, we obtain the spin-wave spectra for experimentally relevant parameters without further approximation by numerical diagonalization, using efficient Ewald summation techniques to carry out the dipolar sums. We compare our numerical results with two different analytic approximations and with predictions based on the phenomenological Landau-Lifshitz equation.

We re-examine the 1/S-correction to the self-energy of the gapless magnon of a D-dimensional quantum Heisenberg antiferromagnet in a uniform magnetic field h using a hybrid approach between 1/S-expansion and non-linear sigma model, where the Holstein-Primakoff bosons are expressed in terms of Hermitian field operators representing the uniform and the staggered components of the spin-operators [N. Hasselmann and P. Kopietz, Europhys. Lett. 74, 1067 (2006)]. By integrating over the field associated with the uniform spin-fluctuations we obtain the effective action for the staggered spin-fluctuations on the lattice, which contains fluctuations on all length scales and does not have the cutoff ambiguities of the non-linear sigma model. We show that in dimensions D ≤ 3 the magnetic field dependence of the spin-wave velocityc−(h) is non-analytic in h 2 , withc−(h)−c−(0) ∝ h 2 ln |h| in D = 3, andc−(h) −c−(0) ∝ |h| in D = 2. The frequency dependent magnon self-energy is found to exhibit an even more singular magnetic field dependence, implying a strong momentum dependence of the quasi-particle residue of the gapless magnon. We also discuss the problem of spontaneous magnon decay and show that in D > 1 dimensions the damping of magnons with momentum k is proportional to |k| 2D−1 if spontaneous magnon decay is kinematically allowed.

We use the Gross-Pitaevskii equation to determine the spatial structure of the condensate density of interacting bosons whose energy dispersion k has two degenerate minima at finite wave-vectors ±q. We show that in general the Fourier transform of the condensate density has finite amplitudes for all integer multiples of q. If the interaction is such that many Fourier components contribute, the Bose condensate is localized at the sites of a one-dimensional lattice with spacing 2π/|q|; in this case Bose-Einstein condensation resembles the transition from a liquid to a crystalline solid. We use our results to investigate the spatial structure of the Bose condensate formed by magnons in thin films of ferromagnets with dipole-dipole interactions.PACS. 03.75.Hh Static properties of condensates; thermodynamical, statistical, and structural properties 75.10.JmQuantized spin models -75.30.Ds Spin waves arXiv:1007.3200v3 [cond-mat.quant-gas]

We present structural and magnetic data of a new Cu(2+)(S = 1/2)-containing magnetic trimer system 2b·3CuCl(2)·2H(2)O (b = betaine, C(5)H(11)NO(2)). The trimers form a quasi-2D quantum spin system with an unusual intra-layer exchange coupling topology, which, in principle, supports diagonal four-spin exchange. To describe the magnetic properties, a 2D effective interacting-trimer model has been developed including an intra-trimer coupling J and two inter-trimer couplings J(a) and J(b). The low-energy description and effective parameters are obtained from numerical calculations based on four coupled trimers (with periodic boundary conditions). Fits to the experimental data using this model yield the magnetic coupling constants J/k(B) = -15 K and J(a)/k(B) = J(b)/k(B) = -4 K. These parameters describe the susceptibility and magnetization data very well over the whole temperature and field range investigated. Moreover, the model calculations indicate that, for certain ranges of the ratio J(b)/J(a), which might be accessible by either chemical substitution and/or hydrostatic pressure, the low-energy properties of 2b·3CuCl(2)·2H(2)O will be dominated by non-trivial four-spin exchange processes.

We show that in two dimensions (2D) a systematic expansion of the self-energy and the effective interaction of the dilute electron gas in powers of the two-body T -matrix T0 can be generated from the exact hierarchy of functional renormalization group equations for the one-particle irreducible vertices using the chemical potential as flow parameter. Due to the interference of particle-particle and particle-hole channels at order T 2 0 , in 2D the ladder approximation for the self-energy is not reliable beyond the leading order in T0. We also discuss two-body scattering in vacuum in arbitrary dimensions from the renormalization group point of view and argue that the singular interaction proposed by Anderson [Phys. Rev. Lett. 65, 2306(1990] cannot be ruled out on the basis of the ladder approximation.PACS numbers: 71.10. Ca, 71.10.Hf, 73.43.Nq Calculating the physical properties of strongly interacting electrons in two spatial dimensions (2D) remains one of the big challenges of condensed matter theory. Most authors agree that the normal state of interacting electrons in 2D is a Fermi liquid, at least for weak interactions. There are even rigorous proofs that at weak coupling certain two-dimensional models for interacting electrons (including the repulsive Hubbard model away from half filling) are Fermi liquids above an energy scale which is non-perturbative in the coupling constant [1]. However, due to a lack of controlled methods, one cannot exclude the possibility that for sufficiently strong interactions Fermi liquid theory breaks down in 2D. Anderson has argued repeatedly [2, 3] that due to non-perturbative effects which are neglected by the usual field-theoretical machinery of many-body theory, the normal state of the two-dimensional Hubbard model is not a Fermi liquid for arbitrary strength of the interaction. This scenario has been criticized early on by Engelbrecht and Randeria [4], who pointed out that a calculation of the selfenergy Σ(k, ω) within the ladder approximation (LAP) predicts Fermi liquid behavior. However, the LAP has some rather peculiar and most likely unphysical features; in particular, the limiting behavior of Σ(k, ω) for small frequencies ω and for wave-vectors k in the vicinity of the Fermi surface k F is very sensitive to the order in which the limits ω → 0 and k → k F are taken [5,6].Unfortunately, going beyond the LAP is very difficult, because the particle-hole scattering channels have to be taken into account on the same footing with the particleparticle scattering channel retained within the LAP, i.e., one has to solve coupled Bethe-Salpeter equations in several channels. In this work we shall take a fresh look at this problem using a formally exact hierarchy for renormalization group (RG) flow equations for the one-particle irreducible vertices [7].Functional RG in the spin-singlet channel. Starting point of our analysis are the formally exact RG flow equations for the irreducible self-energy Σ Λ (K) and the antisymmetrized effective interaction vertex Γ (4)