A fast time domain solver for the equilibrium Dyson equation

Kaye, JasonCenter for Computational Mathematics, Flatiron Institute, New York NY, USA; Center for Computational Quantum Physics, Flatiron Institute, New York NY, USA (author)

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.

Strand, Hugo U. R.,1983- (author)
Center for Computational Mathematics, Flatiron Institute, New York NY, USA; Center for Computational Quantum Physics, Flatiron Institute, New York NY, USA (creator_code:org_t)

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