Krylov-space approach to the equilibrium and the nonequilibrium single-particle Green's function

The zero-temperature single-particle Green's function of correlated fermion models with moderately large Hilbert-space dimensions can be calculated by means of Krylov-space techniques. The conventional Lanczos approach consists of finding the ground state in a first step, followed by an approximation for the resolvent of the Hamiltonian in a second step. We analyze the character of this approximation and discuss a numerically exact variant of the Lanczos method which is formulated in the time domain. This method is extended to get the nonequilibrium single-particle Green's function defined on the Keldysh-Matsubara contour in the complex time plane. The proposed method will be important as an exact-diagonalization solver in the context of self-consistent or variational cluster-embedding schemes. For the recently developed nonequilibrium cluster-perturbation theory, we discuss the efficient implementation and demonstrate the feasibility of the Krylov-based solver. The dissipation of a strong local magnetic excitation into a non-interacting bath is considered as an example for applications.Comment: 20 pages, 5 figures, v2 with minor corrections, JPCM in pres

Non-equilibrium cluster-perturbation theory

The cluster perturbation theory (CPT) is one of the simplest but systematic quantum cluster approaches to lattice models of strongly correlated electrons with local interactions. By treating the inter-cluster potential, in addition to the interactions, as a perturbation, it is shown that the CPT can be reformulated as an all-order re-summation of diagrams within standard weak-coupling perturbation theory where vertex corrections are neglected. This reformulation is shown to allow for a straightforward generalization of the CPT to the general non-equilibrium case using contour-ordered Green's functions. Solving the resulting generalized CPT equation on the discretized Keldysh-Matsubara time contour, the transient dynamics of an essentially arbitrary initial pure or mixed state can be traced. In this way, the time-dependent expectation values of one-particle observables can be obtained within an approximation that neglects spatial correlations beyond the extension of the reference cluster. The necessary computational effort is very moderate. A detailed discussion and simple test calculations are presented to demonstrate the strengths and the shortcomings of the proposed approach. The non-equilibrium CPT is systematic and is controlled in principle by the inverse cluster size. It interpolates between the non-interacting and the atomic or decoupled-cluster limit which are recovered exactly and is found to predict the correct dynamics at very short times in a general non-trivial case. The effects of initial-state correlations on the subsequent dynamics and the necessity to extend the Keldysh contour by the imaginary Matsubara branch are analyzed carefully and demonstrated numerically. It is furthermore shown that the approach can describe the dissipation of spin and charge to an uncorrelated bath with an essentially arbitrary number of degrees of freedom.Comment: 14 pages, 9 figure

Disorder- and correlation-driven metal-insulator transitions

Metal-insulator transitions driven by disorder (Delta) and/or by electron correlations (U) are investigated within the Anderson-Hubbard model with local binary-alloy disorder using a simple but consistent mean-field approach. The Delta-U phase diagram is derived and discussed for T=0 and finite temperatures.Comment: 2 pages, 2 figures, submitted to the SCES'04, Ref.4 update

Parallel implementation of the non-smooth contact dynamics method for large particle systems

In numerous industrial applications there is the need to realistically model granular material. For instance, simulating the interaction of vehicles and tools with soil is of great importance for the design of earth moving machinery. The Discrete Element Method (DEM) has been successfully applied to this task [1, 2]. Large scale problems require a lot of computational resources. Hence, for the application in the industrial engineering process, the computational effort is an issue. In DEM parallelization is straight forward, since each contact between adjacent particles is resolved locally without regard of the other contacts. However, modelling a contact as a stiff spring imposes strong limitations on the time step size to maintain a stable simulation. The Non–Smooth Contact Dynamics Method (NSCD), on the other hand, models contacts globally as a set of inequality constraints on a system of perfectly rigid bodies [3]. At the end of every time step, all inequality constraints must be satisfied simultaneously, which can be achieved by solving a complementarity problem. This leads to a numerically stable method that is robust with respect to much larger time steps in comparison to DEM. Since a global problem must be solved, parallelization now strongly depends on the numerical solver that is used for the complementarity problem. We present our first massively parallel implementation of NSCD based on the projected Gauß-Jacobi (PGJ) iterative scheme presented in [4]. Focusing on one-sided asynchronous communication patterns with double buffering for data exchange, global synchronizations can be avoided. Only weak synchronization due to data dependencies of neighboring domains remains. The implementation is based on the Global address space Programming Interface (GPI), supplemented by the Multi Core Threading Package (MCTP) [5] on the processor level. This allows to efficiently overlap calculation and communication between processors

Mott transition in one dimension: Benchmarking dynamical cluster approaches

The variational cluster approach (VCA) is applied to the one-dimensional Hubbard model at zero temperature using clusters (chains) of up to ten sites with full diagonalization and the Lanczos method as cluster solver. Within the framework of the self-energy-functional theory (SFT), different cluster reference systems with and without bath degrees of freedom, in different topologies and with different sets of variational parameters are considered. Static and one-particle dynamical quantities are calculated for half-filling as a function of U as well as for fixed U as a function of the chemical potential to study the interaction- and filling-dependent metal-insulator (Mott) transition. The recently developed Q-matrix technique is used to compute the SFT grand potential. For benchmarking purposes we compare the VCA results with exact results available from the Bethe ansatz, with essentially exact dynamical DMRG data, with (cellular) dynamical mean-field theory and full diagonalization of isolated Hubbard chains. Several issues are discussed including convergence of the results with cluster size, the ability of cluster approaches to access the critical regime of the Mott transition, efficiency in the optimization of correlated-site vs. bath-site parameters and of multi-dimensional parameter optimization. We also study the role of bath sites for the description of excitation properties and as charge reservoirs for the description of filling dependencies. The VCA turns out to be a computationally cheap method which is competitive with established cluster approaches.Comment: 19 pages, 19 figures, v3 with minor corrections, extended discussio

Airborne in situ vertical profiling of HDO / H216O in the subtropical troposphere during the MUSICA remote sensing validation campaign

Vertical profiles of water vapor (H2O) and its isotope ratio D / H expressed as δD(H2O) were measured in situ by the ISOWAT II diode-laser spectrometer during the MUlti-platform remote Sensing of Isotopologues for investigating the Cycle of Atmospheric water (MUSICA) airborne campaign. We present recent modifications of the instrument design. The instrument calibration on the ground as well as in flight is described. Based on the calibration measurements, the humidity-dependent uncertainty of our airborne data is determined. For the majority of the airborne data we achieved an accuracy (uncertainty of the mean) of Δ(δD) ≈10‰. Vertical profiles between 150 and ~7000 m were obtained during 7 days in July and August 2013 over the subtropical North Atlantic Ocean near Tenerife. The flights were coordinated with ground-based (Network for the Detection of Atmospheric Composition Change, NDACC) and space-based (Infrared Atmospheric Sounding Interferometer, IASI) FTIR remote sensing measurements of δD(H2O) as a means to validate the remote sensing humidity and δD(H2O) data products. The results of the validation are presented in detail in a separate paper (Schneider et al., 2014). The profiles were obtained with a high vertical resolution of around 3 m. By analyzing humidity and δD(H2O) correlations we were able to identify different layers of air masses with specific isotopic signatures. The results are discussed.The MUSICA airborne mission was funded in part by the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no. 256961

Penta­carbonyl-2κ5 C-chlorido-1κCl-bis­[1(η5)-cyclo­penta­dien­yl](μ-α-oxido­benzyl­idene-1:2κ2 O:C)titanium(IV)tungsten(0)

The title compound, [TiW(C5H5)2(C7H5O)Cl(CO)5], consists of two metal centres, with a (tungstenpenta­carbon­yl)oxy­phenyl­carbene unit coordinated by a titanocene chloride. The oxycarbene group is nearly planar, with the phenyl ring twisted by an angle of 39.1 (2)° with respect to this plane. One of the cyclo­penta­dienyl rings undergoes an offset face-to-face π–π inter­action [3.544 (6) Å] with the symmetry-related cyclo­penta­dienyl ring of a neighbouring mol­ecule