arXiv subjects

Hartmut Monien

Publications and source records attributed to Hartmut Monien.

27 records · Page 2Linked to original sources

arXiv2006

Gaussian Summation: An Exponentially Converging Summation Scheme

Gaussian Quadrature is a well known technique for numerical integration. Recently Gaussian quadrature with respect to discrete measures corresponding to finite sums have found some new interest. In this paper we apply these ideas to infinite sums in general and give an explicit construction for the weights and abscissae of GAUSSIAN SUMMATION formulas. The abscissae of the Gaussian summation have a very interesting asymptotic distribution function with a (cusp) singularity. We apply the Gaussian summation technique to two problems which have been discussed in the literature. We find that the Gaussian summation has an extremely rapid convergence rate for the Hardy-Littlewood sum for a large range of parameters. For functions which are smooth but have a large scale, a, the error of Gaussian Summation shows exponential convergence as a function of summation points. The Gaussian summation achieves a given accuracy with a number of points proportional to the sqrt of the large scale whereas other summation schemes require at least a number of function evaluations proportional to the scale.

math.NA↗

arXiv2006

From Mott Insulator to Band Insulator: A DMFT Study

The question if a Mott insulator and a band insulator are fundamentally different has been the matter of intensive research recently. Here we consider a simple model which allows by tuning one parameter to go continously from a Mott insulator to band insulator. The model consists of two Hubbard systems connected by single particle hopping. The Hubbard Hamiltonian is solved by the Dynamical Mean-Field theory using Quantum Monte Carlo to solve the resulting quantum impurity problem. The quasiparticle spectral function is calculated. Here we focus on the optical conductivity and in particular on the Drude weight which can be experimentally measured. From our calculation we conclude that there is a continous crossover from the band insulator to the Mott insulator phase at finite temperature.

cond-mat.str-el↗

arXiv2005

Quasiparticle Dynamics in the Kondo Lattice Model at Half Filling

We study spectral properties of quasiparticles in the Kondo lattice model in one and two dimensions including the coherent quasiparticle dispersions, their spectral weights and the full two-quasiparticle spectrum using a cluster expansion scheme. We investigate the evolution of the quasiparticle band as antiferromagnetic correlations are enhanced towards the RKKY limit of the model. In both the 1D and the 2D model we find that a repulsive interaction between quasiparticles results in a distinct antibound state above the two-quasiparticle continuum. The repulsive interaction is correlated with the emerging antiferromagnetic correlations and can therefore be associated with spin fluctuations. On the square lattice, the antibound state has an extended s-wave symmetry.

cond-mat.str-el↗

arXiv2001

What is wrong with paramagnons?

Systems with itinerant fermions close to a zero temperature quantum phase transition like the high temperature superconductors exhibit unusual non-Fermi liquid properties. The interaction of the long-range and low-energy fluctuations of the incipient order with the fermions modify the dynamical properties of the fermions strongly by inducing effective long-range interactions. Close to the transition the interaction of the order parameter fluctuations becomes important. In this paper we discuss the physics of the non-Gaussian order parameter fluctuations on the electronic spectrum and illustrate their effect by considering the charge-density-wave transition and the phase fluctuations in a two-dimensional d-wave superconductor.

cond-mat.str-el↗

arXiv2001

Exact Results for the Crossover from Gaussian to Non-Gaussian Order Parameter Fluctuations in Quasi One-Dimensional Electronic Systems

The physics of quasi one-dimensional Peierls systems is dominated by order parameter fluctuations. We present an algorithm which allows for the first time to exactly calculate physical properties of the electrons gas coupled to classical order parameter fluctuations. The whole range from the Gaussian regime dominated by amplitude fluctuations to the non-Gaussian regime dominated by phase fluctuations is accessible. Our results provide insight into the 'pseudogap' phenomenon occurring in underdoped high-temperature superconductors, quasi one-dimensional organic conductors and liquid metals.

cond-mat.str-el↗

arXiv2001

Phenomenological theory of the 3 Kelvin phase in Sr2RuO4

We model the 3K-phase of Sr2RuO4 with Ru-metal inclusion as interface state with locally enhanced transition temperatures. The resulting 3K-phase must have a different pairing symmetry than the bulk phase of Sr2RuO4, because the symmetry at the interface is lower than in the bulk. It is invariant under time reversal and a second transition, in general, above the onset of bulk superconductivity is expected where time reversal symmetry is broken. The nucleation of the 3K-phase exhibits a ``capillary effect'' which can lead to frustration phenomena for the superconducting states on different Ru-inclusions. Furthermore, the phase structure of the pair wave function gives rise to zero-energy quasiparticle states which would be visible in quasiparticle tunneling spectra. Additional characteristic properties are associated with the upper critical field Hc2. The 3K-phase has a weaker anisotropy of Hc2 between the inplane and z-axis orientation than the bulk superconducting phase. This is connected with the more isotropic nature Ru-metal which yields a stronger orbital depairing effect for the inplane magnetic field than in the strongly layered Sr$_2RuO4. An anomalous temperature dependence for the z-axis critical field is found due to the coupling of the magnetic field to the order parameter texture at the interface. Various other experiments are discussed and new measurements are suggested.

cond-mat.str-el↗

arXiv2000

Linked Cluster Series Expansions for Two-Particle Bound States

We develop strong-coupling series expansion methods to study two-particle spectra of quantum lattice models. At the heart of the method lies the calculation of an effective Hamiltonian in the two-particle subspace. We explicitly consider an orthogonality transformation to generate this block diagonalization, and find that maintaining orthogonality is crucial for systems where the ground state and the two-particle subspace are characterized by identical quantum numbers. We discuss the solution of the two-particle Schrödinger equation by using a finite lattice approach in coordinate space or by an integral equation in momentum space. These methods allow us to precisely determine the low-lying excitation spectra of the models at hand, including all two-particle bound/antibound states. Further, we discuss how to generate series expansions for the dispersions of the bound/antibound states. These allow us to employ series extrapolation techniques, whereby binding energies can be determined even when the expansion parameters are not small. We apply the method to the (1+1)D transverse Ising model and the two-leg spin-$\case 1/2$ Heisenberg ladder. For the latter model, we also calculate the coherence lengths and determine the critical properties where bound states merge with the two-particle continuum.

cond-mat.str-el↗

arXiv2000

Deconfinement Transition and Bound States in Frustrated Heisenberg Chains: Regimes of Forced and Spontaneous Dimerization

We use recently developed strong-coupling expansion methods to study the two-particle spectra for the frustrated alternating Heisenberg model, consisting of an alternating nearest neighbor antiferromagnetic exchange and a uniform second neighbor antiferromagnetic exchange. Starting from the limit of weakly coupled dimers, we develop high order series expansions for the effective Hamiltonian in the two-particle subspace. In the limit of a strong applied dimerization, we calculate accurately various properties of singlet and triplet bound states and quintet antibound states. We also develop series expansions for bound state energies in various sectors, which can be extrapolated using standard methods to cases where the external bond-alternation goes to zero. We study the properties of singlet and triplet bound states in the latter limit and suggest a crucial role for the bound states in the unbinding of triplets and deconfinement of spin-half excitations.

cond-mat.str-el↗

arXiv1999

A numerical exact solution of the Bose-Hubbard model

In this paper we report results from a systematic strong-coupling expansion of the Bose-Hubbard model in one and two spatial dimensions. We obtain numerically exact results for the structure factor and the spectrum of single particle and single hole excitations in the Mott insulator. This enables the determination of the zero-temperature phase diagram and the location of the critical endpoints of the Mott lobes. In one dimension we confirm the occurrence of reentrance behavior from the compressible to the insulating phase in a region close to the critical point.

cond-mat.supr-con↗