Hybridization expansion impurity solver: General formulation and application to Kondo lattice and two-orbital models

A recently developed continuous time solver based on an expansion in hybridization about an exactly solved local limit is reformulated in a manner appropriate for general classes of quantum impurity models including spin exchange and pair hopping terms. The utility of the approach is demonstrated via applications to the dynamical mean field theory of the Kondo lattice and two-orbital models. The algorithm can handle low temperatures and strong couplings without encountering a sign problem.Comment: Published versio

Low temperature properties of the infinite-dimensional attractive Hubbard model

We investigate the attractive Hubbard model in infinite spatial dimensions by combining dynamical mean-field theory with a strong-coupling continuous-time quantum Monte Carlo method. By calculating the superfluid order parameter and the density of states, we discuss the stability of the superfluid state. In the intermediate coupling region above the critical temperature, the density of states exhibits a heavy fermion behavior with a quasi-particle peak in the dense system, while a dip structure appears in the dilute system. The formation of the superfluid gap is also addressed.Comment: 8 pages, 9 figure

On the limitations of cRPA downfolding

We check the accuracy of the constrained random phase approximation (cRPA) downfolding scheme by considering one-dimensional two- and three-orbital Hubbard models with a target band at the Fermi level and one or two screening bands away from the Fermi level. Using numerically exact quantum Monte Carlo simulations of the full and downfolded model we demonstrate that depending on filling the effective interaction in the low-energy theory is either barely screened, or antiscreened, in contrast to the cRPA prediction. This observation is explained by a functional renormalization group analysis which shows that the cRPA contribution to the screening is to a large extent cancelled by other diagrams in the direct particle-hole channel. We comment on the implications of this finding for the ab-initio estimation of interaction parameters in low-energy descriptions of solids

Non-perturbative theoretical description of two atoms in an optical lattice with time-dependent perturbations

A theoretical approach for a non-perturbative dynamical description of two interacting atoms in an optical lattice potential is introduced. The approach builds upon the stationary eigenstates found by a procedure described in Grishkevich et al. [Phys. Rev. A 84, 062710 (2011)]. It allows presently to treat any time-dependent external perturbation of the lattice potential up to quadratic order. Example calculations of the experimentally relevant cases of an acceleration of the lattice and the turning-on of an additional harmonic confinement are presented.Comment: 8 pages, 6 figure

Performance analysis of continuous-time solvers for quantum impurity models

Impurity solvers play an essential role in the numerical investigation of strongly correlated electrons systems within the "dynamical mean field" approximation. Recently, a new class of continuous-time solvers has been developed, based on a diagrammatic expansion of the partition function in either the interactions or the impurity-bath hybridization. We investigate the performance of these two complementary approaches and compare them to the well-established Hirsch-Fye method. The results show that the continuous-time methods, and in particular the version which expands in the hybridization, provide substantial gains in computational efficiency

Probabilistic Linear Solvers: A Unifying View

Several recent works have developed a new, probabilistic interpretation for numerical algorithms solving linear systems in which the solution is inferred in a Bayesian framework, either directly or by inferring the unknown action of the matrix inverse. These approaches have typically focused on replicating the behavior of the conjugate gradient method as a prototypical iterative method. In this work surprisingly general conditions for equivalence of these disparate methods are presented. We also describe connections between probabilistic linear solvers and projection methods for linear systems, providing a probabilistic interpretation of a far more general class of iterative methods. In particular, this provides such an interpretation of the generalised minimum residual method. A probabilistic view of preconditioning is also introduced. These developments unify the literature on probabilistic linear solvers, and provide foundational connections to the literature on iterative solvers for linear systems

On the Complexity of Reconstructing Chemical Reaction Networks

The analysis of the structure of chemical reaction networks is crucial for a better understanding of chemical processes. Such networks are well described as hypergraphs. However, due to the available methods, analyses regarding network properties are typically made on standard graphs derived from the full hypergraph description, e.g.\ on the so-called species and reaction graphs. However, a reconstruction of the underlying hypergraph from these graphs is not necessarily unique. In this paper, we address the problem of reconstructing a hypergraph from its species and reaction graph and show NP-completeness of the problem in its Boolean formulation. Furthermore we study the problem empirically on random and real world instances in order to investigate its computational limits in practice