arXiv subjects

N. Hasselmann

Publications and source records attributed to N. Hasselmann.

15 recordsLinked to original sources

arXiv2014

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.

cond-mat.stat-mech↗

arXiv2012

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.

cond-mat.mes-hall↗

arXiv2012

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.

cond-mat.stat-mech↗

arXiv2011

Nonlocal effective average action approach to crystalline phantom membranes

We investigate the properties of crystalline phantom membranes, at the crumpling transition and in the flat phase, using a nonperturbative renormalization group approach. We avoid a derivative expansion of the effective average action and instead analyse the full momentum dependence of the elastic coupling functions. This leads to a more accurate determination of the critical exponents and further yields the full momentum dependence of the correlation functions of the in-plane and out-of-plane fluctuation. The flow equations are solved numerically for D=2 dimensional membranes embedded in a d=3 dimensional space. Within our approach we find a crumpling transition of second order which is characterized by an anomalous exponent $η_c\approx 0.63(8)$ and the thermal exponent $ν\approx 0.69$. Near the crumpling transition the order parameter of the flat phase vanishes with a critical exponent $β\approx 0.22$. The flat phase anomalous dimension is $η_f\approx 0.85$ and the Poisson's ratio inside the flat phase is found to be $σ_f\approx -1/3$. At the crumpling transition we find a much larger negative value of the Poisson's ratio $σ_c \approx -0.71(5)$. We discuss further in detail the different regimes of the momentum dependent fluctuations, both in the flat phase and in the vicinity of the crumpling transition, and extract the crossover momentum scales which separate them.

cond-mat.stat-mech↗

arXiv2010

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.

cond-mat.soft↗

arXiv2004

Approximative treatment of 5f-systems with partial localization due to intra-atomic correlations

Increasing experimental and theoretical evidence points towards a dual nature of the 5$f$ electrons in actinide-based strongly correlated metallic compounds, with some 5$f$ electrons being localized and others delocalized. In a recent paper (PRB xxx, 2004), we suggested the interplay of intra-atomic correlations as described by Hund's rules and a weakly anisotropic hopping (hybridization) as a possible mechanism. The purpose of the present work is to provide a first step towards a microscopic description of partial localization in solids by analyzing how well various approximation schemes perform when applied to small clusters. It is found that many aspects of partial localization are described appropriately both by a variational wavefunction of Gutzwiller type and by a treatment which keeps only those interactions which are present in LDA+U calculations. In contrast, the energies and phase diagram calculated within the Hartree Fock approximation show little resemblence with the exact results. Enhancement of hopping anisotropy by Hund's rule correlations are found in all approximations.

cond-mat.str-el↗

arXiv2003

Spin-glass phase of cuprates

We investigate a phenomenological model for the spin glass phase of La_{2-x}Sr_xCuO_4, in which it is assumed that holes doped into the CuO_2 planes localize near their Sr dopant, where they cause a dipolar frustration of the antiferromagnetic environment. In absence of long-range antiferromagnetic order, the spin system can reduce frustration, and also its free energy, by forming a state with an ordered orientation of the dipole moments, which leads to the appearance of spiral spin correlations. To investigate this model, a non-linear sigma model is used in which disorder is introduced via a randomly fluctuating gauge field. A renormalization group study shows that the collinear fixed point of the model is destroyed through the disorder and that the disorder coupling leads to an additive renormalization of the order parameter stiffness. Further, the stability of the spiral state against the formation of topological defects is investigated with the use of the replica trick. A critical disorder strength is found beyond which topological defects proliferate. Comparing our results with experimental data, it is found that for a hole density x > 0.02, i.e. in the entire spin glass regime, the disorder strength exceeds the critical threshold. In addition, some experiments are proposed in order to distinguish if the incommensurabilities observed in neutron scattering experiments correspond to a diagonal stripe or a spiral phase.

cond-mat.dis-nn↗

arXiv2003

On a dual model for 5f electrons

We study the effect of intra-atomic correlations on anisotropies of hopping of 5f electrons. It is shown that they may considerably enhance these anisotropies to the extend that electrons in some of the 5f orbitals remain localized. This provide a microscopic basis for a previously made assumption that some of the 5f electrons must be partially localized when Fermi surfaces and effective masses of the component are calculated. Calculations are performed on two- and three-sites clusters. They include phase diagrams in the presence and absence of an external magnetic field as function of anisotropic hopping.

cond-mat↗

arXiv2001

Charge Density Wave Formation in the Low-Temperature-Tetragonal Phase of Cuprates

We calculate the influence of transverse fluctuations on the longitudinal dynamics in the striped phase of cuprates by using the bosonization technique. We find that a charge density wave instability can arise if the stripe is quarter filled and the underlying lattice potential has a zigzag symmetry. Our results explain why static stripes are experimentally observed in underdoped La_{2-x-y}Nd_ySr_xCuO_4 exactly at the onset of the low-temperature-tetragonal transition.

cond-mat.str-el↗

arXiv2001

Topological Defects and the Spin Glass Phase of Cuprates

We propose that the spin glass phase of cuprates is due to the proliferation of topological defects of a spiral distortion of the antiferromagnet order. Our theory explains straightforwardly the simultaneous existence of short range incommensurate magnetic correlations and complete a-b symmetry breaking in this phase. We show via a renormalization group calculation that the collinear O(3)/O(2) symmetry is unstable towards the formation of local non-collinear correlations. A critical disorder strength is identified beyond which topological defects proliferate already at zero temperature.

cond-mat.dis-nn↗

arXiv2000

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.

cond-mat.str-el↗

arXiv1999

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.

cond-mat.soft↗

arXiv1999

Dynamics of lattice pinned charge stripes

We study the transversal dynamics of a charged stripe (quantum string) and show that zero temperature quantum fluctuations are able to depin it from the lattice. If the hopping amplitude t is much smaller than the string tension J, the string is pinned by the underlying lattice. At t>>J, the string is depinned and allowed to move freely, if we neglect the effect of impurities. By mapping the system onto a 1D array of Josephson junctions, we show that the quantum depinning occurs at t/J = 2 / pi^2. Besides, we exploit the relation of the stripe Hamiltonian to the sine-Gordon theory and calculate the infrared excitation spectrum of the quantum string for arbitrary t/J values.

cond-mat.soft↗

arXiv1999

The Striped Phase in Presence of Disorder and Lattice Potentials

We study the influence of disorder and lattice effects on the striped phase and the incommensurate spin fluctuations of the cuprates and nickelates. Starting from a phenomenological model of a discrete quantum string on a lattice with disorder, we derive the renormalisation group equations in leading order in the lattice and disorder strength. Three regimes are identified, the quantum membrane phase, the flat phase pinned by the lattice and the disorder pinned phase. We compare our results with measurements on nickelates and cuprates and find good agreement.

cond-mat.str-el↗

arXiv1997

Dynamics of Stripes in Doped Antiferromagnets

We study the dynamics of the striped phase, which has previously been suggested to be the ground state of a doped antiferromagnet. Starting from the t-J model, we derive the classical equation governing the motion of the charged wall by using a ficticious spin model as an intermediate step. A wave-like equation of motion is obtained and the wall elasticity and mass density constants are derived in terms of the t and J parameters. The wall is then regarded as an elastic string which will be trapped by the pinning potential produced by randomly distributed impurities. We evaluate the pinning potential and estimate the threshold electric field which has to be applied to the system in order to release the walls. Besides, the dynamics of the stripe in the presence of a bias field below the threshold is considered and the high- and low-temperature relaxation rates are derived.

cond-mat↗