A fast time domain solver for the equilibrium Dyson equation

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 standard fast algorithms. propose quasilinear-scaling FFT-based algorithm respects operator. The resulting method reach large propagation times, and thus well-suited to explore phenomena at low energy scales. demonstrate solver with two model systems: Bethe graph, Sachdev-Ye-Kitaev model.