arXiv subjects

Alexander Weisse

Publications and source records attributed to Alexander Weisse.

13 recordsLinked to original sources

arXiv2018

Records on the vanishing of Fourier coefficients of Powers Of the Dedekind Eta Function

In this paper we significantly extend Serre's table on the vanishing properties of Fourier coefficients of odd powers of the Dedekind eta function. We address several conjectures of Cohen and Strömberg and give a partial answer to a question of Ono. In the even-power case, we extend Lehmer's conjecture on the coefficients of the discriminant function $Δ$ to all non-CM-forms. All our results are supported with numerical data. For example all Fourier coefficients $a_9(n)$ of the $9$-th power of the Dedekind eta function are non-vanishing for $n \leq 10^{10}$. We also relate the non-vanishing of the Fourier coefficients of $Δ^2$ to Maeda's conjecture.

math.NT↗

arXiv2006

Phase diagram of the spin-Peierls chain with local coupling

We explore the ground-state phase diagram of a Heisenberg spin chain coupled locally to optical phonons (bond coupling), using large-scale density matrix renormalization group calculations and an extended perturbative analysis. For the quantum phase transition from the spin liquid to the dimerized phase, we find deviations from previous quantum Monte Carlo and flow equation results.

cond-mat.str-el↗

arXiv2006

The spin-Peierls chain revisited

We extend previous analytical studies of the ground-state phase diagram of a one-dimensional Heisenberg spin chain coupled to optical phonons, which for increasing spin-lattice coupling undergoes a quantum phase transition from a gap-less to a gaped phase with finite lattice dimerisation. We check the analytical results against established four-block and new two-block density matrix renormalisation group (DMRG) calculations. Different finite-size scaling behaviour of the spin excitation gaps is found in the adiabatic and anti-adiabatic regimes.

cond-mat.str-el↗

arXiv2006

The Kernel Polynomial Method

Efficient and stable algorithms for the calculation of spectral quantities and correlation functions are some of the key tools in computational condensed matter physics. In this article we review basic properties and recent developments of Chebyshev expansion based algorithms and the Kernel Polynomial Method. Characterized by a resource consumption that scales linearly with the problem dimension these methods enjoyed growing popularity over the last decade and found broad application not only in physics. Representative examples from the fields of disordered systems, strongly correlated electrons, electron-phonon interaction, and quantum spin systems we discuss in detail. In addition, we illustrate how the Kernel Polynomial Method is successfully embedded into other numerical techniques, such as Cluster Perturbation Theory or Monte Carlo simulation.

cond-mat.other↗

arXiv2005

Comparative numerical study of Anderson localization in disordered electron systems

Taking into account that a proper description of disordered systems should focus on distribution functions, the authors develop a powerful numerical scheme for the determination of the probability distribution of the local density of states (LDOS), which is based on a Chebyshev expansion with kernel polynomial refinement and allows the study of large finite clusters (up to $100^3$). For the three-dimensional Anderson model it is demonstrated that the distribution of the LDOS shows a significant change at the disorder induced delocalisation-localisation transition. Consequently, the so-called typical density of states, defined as the geometric mean of the LDOS, emerges as a natural order parameter. The calculation of the phase diagram of the Anderson model proves the efficiency and reliability of the proposed approach in comparison to other localisation criteria, which rely, e.g., on the decay of the wavefunction or the inverse participation number.

cond-mat.dis-nn↗

arXiv2004

Microscopic modelling of doped manganites

Colossal magneto-resistance manganites are characterised by a complex interplay of charge, spin, orbital and lattice degrees of freedom. Formulating microscopic models for these compounds aims at meeting to conflicting objectives: sufficient simplification without excessive restrictions on the phase space. We give a detailed introduction to the electronic structure of manganites and derive a microscopic model for their low energy physics. Focussing on short range electron-lattice and spin-orbital correlations we supplement the modelling with numerical simulations.

cond-mat.str-el↗

arXiv2004

Optical response of electrons in a random potential

Using our recently developed Chebyshev expansion technique for finite-temperature dynamical correlation functions we numerically study the AC conductivity $σ(ω)$ of the Anderson model on large cubic clusters of up to $100^3$ sites. Extending previous results we focus on the role of the boundary conditions and check the consistency of the DC limit, $ω\to 0$, by comparing with direct conductance calculations based on a Greens function approach in a Landauer Büttiker type setup.

cond-mat.dis-nn↗

arXiv2004

Chebyshev expansion approach to the AC conductivity of the Anderson model

We propose an advanced Chebyshev expansion method for the numerical calculation of linear response functions at finite temperature. Its high stability and the small required resources allow for a comprehensive study of the optical conductivity $σ(ω)$ of non-interacting electrons in a random potential (Anderson model) on large three-dimensional clusters. For low frequency the data follows the analytically expected power-law behaviour with an exponent that depends on disorder and has its minimum near the metal-insulator transition, where also the extrapolated DC conductivity continuously goes to zero. In view of the general applicability of the Chebyshev approach we briefly discuss its formulation for interacting quantum systems.

cond-mat.dis-nn↗

arXiv2004

Unusual localisation effects in quantum percolation

We present a detailed study of the quantum site percolation problem on simple cubic lattices, thereby focussing on the statistics of the local density of states and the spatial structure of the single particle wavefunctions. Using the Kernel Polynomial Method we refine previous studies of the metal-insulator transition and demonstrate the non-monotonic energy dependence of the quantum percolation threshold. Remarkably, the data indicates a ``fragmentation'' of the spectrum into extended and localised states. In addition, the observation of a chequerboard-like structure of the wavefunctions at the band centre can be interpreted as anomalous localisation.

cond-mat.str-el↗

arXiv2004

Delocalisation transition in chains with correlated disorder

We show that in the one-dimensional (1D) Anderson model long-range correlations within the sequence of on-site potentials may lead to a region of extended states in the vicinity of the band centre, i.e., to a correlation-induced insulator-metal transition. Thus, although still disordered, the 1D system can behave as a conductor.

cond-mat.str-el↗

arXiv2004

Spin-lattice coupling effects in the Holstein double-exchange model

Based on the Holstein double-exchange model and a highly efficient single cluster Monte Carlo approach we study the interplay of double-exchange and polaron effects in doped colossal magneto-resistance (CMR) manganites. The CMR transition is shown to be appreciably influenced by lattice polaron formation.

cond-mat.str-el↗

arXiv2003

Lattice and superexchange effects in doped CMR manganites

We report on the influence of the lattice degrees of freedom on charge, orbital and spin correlations in colossal magnetoresistance (CMR) manganites. For the weakly doped compounds we demonstrate that the electron-phonon coupling promotes the trapping of charge carriers, the disappearance of the orbital polaron pattern and the breakdown of ferromagnetism at the CMR transition. The role of different superexchange interactions is explored.

cond-mat.str-el↗

arXiv2002

Interplay of charge, spin, orbital and lattice correlations in colossal magnetoresistance manganites

We derive a realistic microscopic model for doped colossal magnetoresistance manganites, which includes the dynamics of charge, spin, orbital and lattice degrees of freedom on a quantum mechanical level. The model respects the SU(2) spin symmetry and the full multiplet structure of the manganese ions within the cubic lattice. Concentrating on the hole doped domain ($0\le x\le 0.5$) we study the influence of the electron-lattice interaction on spin and orbital correlations by means of exact diagonalisation techniques. We find that the lattice can cause a considerable suppression of the coupling between spin and orbital degrees of freedom and show how changes in the magnetic correlations are reflected in dynamic phonon correlations. In addition, our calculation gives detailed insights into orbital correlations and demonstrates the possibility of complex orbital states.

cond-mat.str-el↗