We use tensor network techniques to obtain high-order perturbative diagrammatic expansions for the quantum many-body problem at very high precision. The approach is based on a train parsimonious representation of sum all Feynman diagrams, obtained in controlled and accurate way with cross interpolation algorithm. It yields full time evolution physical quantities presence any arbitrary time-dependent interaction. Our benchmarks Anderson impurity problem, within real-time nonequilibrium...

We present an efficient basis for imaginary time Green's functions based on a low-rank decomposition of the spectral Lehmann representation. The are simply set well-chosen exponentials, so corresponding expansion may be thought as discrete form representation using effective density which is sum $\ensuremath{\delta}$ functions. determined only by upper bound product $\ensuremath{\beta}{\ensuremath{\omega}}_{max}$, with $\ensuremath{\beta}$ inverse temperature and...

We introduce libdlr, a library implementing the recently introduced discrete Lehmann representation (DLR) of imaginary time Green's functions. The DLR basis consists collection exponentials chosen by interpolative decomposition to ensure stable and efficient recovery functions from or Matsbuara frequency samples. provides subroutines build grids, carry out various standard operations. simplicity makes it straightforward incorporate into existing codes as replacement for less representations...

Abstract We consider the numerical solution of real-time equilibrium Dyson equation, which is used in calculations dynamical properties quantum many-body systems. show that this equation can be written as a system coupled, nonlinear, convolutional Volterra integro-differential equations, for kernel depends self-consistently on solution. As typical Volterra-type computational bottleneck quadratic-scaling cost history integration. However, structure nonlinear integral operator precludes use...

We present a deterministic algorithm for the efficient evaluation of imaginary-time diagrams based on recently introduced discrete Lehmann representation (DLR) Green’s functions. In addition to discretization diagrammatic integrals afforded by its approximation properties, DLR basis is separable in imaginary-time, allowing us decompose into linear combinations nested sequences one-dimensional products and convolutions. Focusing strong-coupling bold-line expansion generalized Anderson...

Several recent works have introduced highly compact representations of single-particle Green's functions in the imaginary time and Matsubara frequency domains, as well efficient interpolation grids used to recover representations. In particular, intermediate representation with sparse sampling discrete Lehmann (DLR) make use low-rank compression techniques obtain optimal approximations controllable accuracy. We consider DLR dynamical mean-field theory (DMFT) calculations, show that standard...

We present a generalization of the discrete Lehmann representation (DLR) to three-point correlation and vertex functions in imaginary time Matsubara frequency. The takes form linear combination judiciously chosen exponentials time, products simple poles frequency, which are universal for given temperature energy cutoff. systematic algorithm generate compact sampling grids, from coefficients such an expansion can be obtained by solving system. show that explicit used evaluate diagrammatic...

Kohn-Sham density functional theory is one of the most widely used electronic structure theories. The recently developed adaptive local basis functions form an accurate and systematically improvable set for solving using discontinuous Galerkin methods, requiring a small number per atom. In this paper we develop residual-based posteriori error estimates approach, which can be to guide non-uniform refinement highly inhomogeneous systems such as surfaces large molecules. are non-polynomial...

We present an efficient method to solve the narrow capture and escape problems for sphere. The problem models equilibrium behavior of a Brownian particle in exterior sphere whose surface is reflective, except collection small absorbing patches. dual problem: it confined interior patches through which can escape. Mathematically, these give rise mixed Dirichlet/Neumann boundary value Poisson equation. They are numerically challenging two main reasons: (1) solutions non-smooth at...

We propose a method to improve the computational and memory efficiency of numerical solvers for nonequilibrium Dyson equation in Keldysh formalism. It is based on empirical observation that Green's functions self energies arising many problems physical interest, discretized as matrices, have low rank off-diagonal blocks, can therefore be compressed using hierarchical data structure. describe an efficient algorithm build this representation fly during course time stepping, use reduce cost...

We show that the amplitude mode in superconductors exhibits chirped oscillations under resonant excitation and chirping velocity increases as we approach critical strength. The enables us to determine local modification of effective potential even when system is a long-lived pre-thermal state. then this an experimentally observable quantity since photo-induced (super)-current pump-probe experiments serves efficient proxy for dynamics order parameter, including dynamics. Our result based on...

We introduce cppdlr, a C++ library implementing the discrete Lehmann representation (DLR) of functions in imaginary time and Matsubara frequency, such as Green's self-energies. The DLR is based on low-rank approximation analytic continuation kernel, yields compact explicit basis consisting exponentials simple poles frequency. cppdlr constructs associated interpolation grids, implements standard operations. It provides flexible yet high-level interface, facilitating incorporation into both...

We present an efficient method for propagating the time-dependent Kohn-Sham equations in free space, based on recently introduced Fourier contour deformation (FCD) approach. For potentials which are constant outside a bounded domain, FCD yields high-order accurate numerical solution of Schrodinger equation directly without need artificial boundary conditions. Of many existing condition schemes, is most similar to exact nonlocal transparent condition, but it works Cartesian grids any...

We introduce a numerical method for the solution of time-dependent Schrodinger equation with smooth potential, based on its reformulation as Volterra integral equation. present versions both periodic boundary conditions, and free space problems compactly supported initial data potential. A spatially uniform electric field may be included, making solver applicable to simulations light-matter interaction. The primary computational challenge in using formulation is application space-time...

We consider the problem of constructing transparent boundary conditions for time-dependent Schrödinger equation with a compactly supported binding potential and, if desired, spatially uniform, electromagnetic vector potential. Such prevent nonphysical effects from corrupting numerical solution in bounded computational domain. use ideas theory to build exact nonlocal arbitrary piecewise-smooth domains. These generalize standard Dirichlet-to-Neumann and Neumann-to-Dirichlet maps known one...

Direct-current resistivity is a key probe for the physical properties of materials. In metals, Fermi-liquid (FL) theory serves as basis understanding transport. A $T^2$ behavior often taken signature FL electron-electron scattering. However, presence impurity and phonon scattering well material-specific aspects such Fermi surface geometry can complicate this interpretation. We demonstrate how density-functional combined with dynamical mean-field be used to elucidate regime. take examples...