Interplay of topology and geometry in frustrated 2d Heisenberg magnets

We investigate two-dimensional frustrated Heisenberg magnets using non-perturbative renormalization group techniques. These magnets allow for point-like topological defects which are believed to unbind and drive either a crossover or a phase transition which separates a low temperature, spin-wave dominated regime from a high temperature regime where defects are abundant. Our approach can account for the crossover qualitatively and both the temperature dependence of the correlation length as well as a broad but well defined peak in the specific heat are reproduced. We find no signatures of a finite temperature transition and an accompanying diverging length scale. Our analysis is consistent with a rapid crossover driven by topological defects.Comment: 12 pages, 8 figures, final version to appear in Physical Review

Thermal fluctuations of free standing graphene

We use non-perturbative renormalization group techniques to calculate the momentum dependence of thermal fluctuations of graphene, based on a self-consistent calculation of the momentum dependent elastic constants of a tethered membrane. We find a sharp crossover from the perturbative to the anomalous regime, in excellent agreement with Monte Carlo results for graphene, and give an accurate value for the crossover scale. Our work strongly supports the notion that graphene is well described as a tethered membrane. Ripples emerge naturally from our analysis.Comment: 5 pages, 2 figures; discussion of the Ginzburg scale of the out-of-plane fluctuations and its relation to ripples was extended. Final version, to appear in PR

Effective average action based approach to correlation functions at finite momenta

We present a truncation scheme of the effective average action approach of the nonperturbative renormalization group which allows for an accurate description of the critical regime as well as of correlation functions at finite momenta. The truncation is a natural modification of the standard derivative expansion which includes both all local correlations and two-point and four-point irreducible correlations to all orders in the derivatives. We discuss schemes for both the symmetric and the symmetry broken phase of the O(N) model and present results for D=3. All approximations are done directly in the effective average action rather than in the flow equations of irreducible vertices. The approach is numerically relatively easy to implement and yields good results for all N both for the critical exponents as well as for the momentum dependence of the two-point function.Comment: 6 pages, 1 figure, 3 table

Functional renormalization group approach to the singlet-triplet transition in quantum dots

We present a functional renormalization group approach to the zero bias transport properties of a quantum dot with two different orbitals and in presence of Hund's coupling. Tuning the energy separation of the orbital states, the quantum dot can be driven through a singlet-triplet transition. Our approach, based on the approach by Karrasch {\em et al} which we apply to spin-dependent interactions, recovers the key characteristics of the quantum dot transport properties with very little numerical effort. We present results on the conductance in the vicinity of the transition and compare our results both with previous numerical renormalization group results and with predictions of the perturbative renormalization group.Comment: 15 pages, 9 figure

Spin-wave interactions in quantum antiferromagnets

We study spin-wave interactions in quantum antiferromagnets by expressing the usual magnon annihilation and creation operators in terms of Hermitian field operators representing transverse staggered and ferromagnetic spin fluctuations. In this parameterization, which was anticipated by Anderson in 1952, the two-body interaction vertex between staggered spin fluctuations vanishes at long wavelengths. We derive a new effective action for the staggered fluctuations only by tracing out the ferromagnetic fluctuations. To one loop order, the renormalization group flow agrees with the nonlinear-$\sigma$-model approach.Comment: 7 pages, no figures; new references added; extended discussion on vertex structure. To appear in Europhysics Letter

Correlated versus Uncorrelated Stripe Pinning: the Roles of Nd and Zn Co-Doping

We investigate the stripe pinning produced by Nd and Zn co-dopants in cuprates via a renormalization group approach. The two dopants play fundamentally different roles in the pinning process. While Nd induces a correlated pinning potential that traps the stripes in a flat phase and suppresses fluctuations, Zn pins the stripes in a disordered manner and promotes line meandering. We obtain the zero temperature phase diagram and compare our results with neutron scattering data. A good agreement is found between theory and experiment.Comment: To appear at the proceedings of the LLD2K Conference Tsukuba, July 2000, Japan. 4 pages, 2 figure

Functional renormalization group in the broken symmetry phase: momentum dependence and two-parameter scaling of the self-energy

We include spontaneous symmetry breaking into the functional renormalization group (RG) equations for the irreducible vertices of Ginzburg-Landau theories by augmenting these equations by a flow equation for the order parameter, which is determined from the requirement that at each RG step the vertex with one external leg vanishes identically. Using this strategy, we propose a simple truncation of the coupled RG flow equations for the vertices in the broken symmetry phase of the Ising universality class in D dimensions. Our truncation yields the full momentum dependence of the self-energy Sigma (k) and interpolates between lowest order perturbation theory at large momenta k and the critical scaling regime for small k. Close to the critical point, our method yields the self-energy in the scaling form Sigma (k) = k_c^2 sigma^{-} (k | xi, k / k_c), where xi is the order parameter correlation length, k_c is the Ginzburg scale, and sigma^{-} (x, y) is a dimensionless two-parameter scaling function for the broken symmetry phase which we explicitly calculate within our truncation.Comment: 9 pages, 4 figures, puplished versio

Stripe dynamics in presence of disorder and lattice potentials

We study the influence of disorder and lattice pinning on the dynamics of a charged stripe. Starting from a phenomenological model of a discrete quantum string, we determine the phase diagram for this system. Three regimes are identified, the free phase, the flat phase pinned by the lattice, and the disorder pinned phase. In the absence of impurities, the system can be mapped onto a 1D array of Josephson junctions. The results are compared with measurements on nickelates and cuprates and a good qualitative agreement is found between our results and the experimental data.Comment: 4 pages, 2 figure