A fast time domain solver for the equilibrium Dyson equation

Abstract

We consider the numerical solution of the real time equilibrium Dyson equation, which is used in calculations of the dynamical properties of quantum many-body systems. We show that this equation can be written as a system of coupled, nonlinear, convolutional Volterra integro-differential equations, for which the kernel depends self-consistently on the solution. As is typical in the numerical solution of Volterra-type equations, the computational bottleneck is the quadratic-scaling cost of history integration. However, the structure of the nonlinear Volterra integral operator precludes the use of standard fast algorithms. We propose a quasilinear-scaling FFT-based algorithm which respects the structure of the nonlinear integral operator. The resulting method can reach large propagation times, and is thus well-suited to explore quantum many-body phenomena at low energy scales. We demonstrate the solver with two standard model systems: the Bethe graph, and the Sachdev-Ye-Kitaev model.

References in corpus (34)

• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Nonequilibrium dynamical mean-field theory and its applications
• The GW compendium: A practical guide to theoretical photoemission spectroscopy
• Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids
• Orthogonal Polynomial Representation of Imaginary-Time Green's Functions
• Notes on the complex Sachdev-Ye-Kitaev model
• The Band-Gap Problem in Semiconductors Revisited: Effects of Core States and Many-Body Self-Consistency
• Compressing Green's function using intermediate representation between imaginary-time and real-frequency domains
• Digital Quantum Simulation of Minimal AdS/CFT
• Fast and oblivious convolution quadrature
• Nevanlinna Analytical Continuation
• NESSi: The Non-Equilibrium Systems Simulation package
• Sparse sampling approach to efficient ab initio calculations at finite temperature
• Time-propagation of the Kadanoff-Baym equations for inhomogeneous systems
• An O(N^3) implementation of Hedin's GW approximation for molecules
• Analytical Continuation of Matrix-Valued Functions: Carathéodory Formalism
• Discrete Lehmann representation of imaginary time Green's functions
• Optical lattice platform for the SYK model
• Diagrammatic expansion for positive spectral functions beyond GW: Application to vertex corrections in the electron gas
• Low rank compression in the numerical solution of the nonequilibrium Dyson equation
• Efficient temperature-dependent Green's functions methods for realistic systems: compact grids for orthogonal polynomial transforms
• Chebyshev polynomial representation of imaginary time response functions
• Robust analytic continuation of Green's functions via projection, pole estimation, and semidefinite relaxation
• Performance analysis of a physically constructed orthogonal representation of imaginary-time Green's function
• libdlr: Efficient imaginary time calculations using the discrete Lehmann representation
• Legendre-spectral Dyson equation solver with super-exponential convergence
• Efficient ab initio many-body calculations based on sparse modeling of Matsubara Green's function
• Beyond the Hubbard bands in strongly correlated lattice bosons
• A scalable numerical approach to the solution of the Dyson equation for the non-equilibrium single-particle Green's function
• Electronic structure of LaNiO${}_2$ and CaCuO${}_2$ from self consistent vertex corrected GW approach
• A high-order integral equation-based solver for the time-dependent Schrodinger equation
• A fast, high-order numerical method for the simulation of single-excitation states in quantum optics
• Transparent Boundary Conditions for the Time-Dependent Schrödinger Equation with a Vector Potential
• Fast integral equation methods for linear and semilinear heat equations in moving domains

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• Stabilizing the calculation of the self-energy in dynamical mean-field theory using constrained residual minimization
• Chirped amplitude mode in photo-excited superconductors
• Discrete Lehmann representation of three-point functions
• cppdlr: Imaginary time calculations using the discrete Lehmann representation
• Towards numerically exact computation of conductivity in the thermodynamic limit of interacting lattice models
• Solving the Transient Dyson Equation with Quasilinear Complexity via Matrix Compression
• Automated evaluation of imaginary time strong coupling diagrams by sum-of-exponentials hybridization fitting
• Stochastic Schrödinger equation approach to real-time dynamics of Anderson-Holstein impurities: an open quantum system perspective