Affiliation:
1. Flatiron Institute
2. Jožef Stefan Institute
3. University of Ljubljana
Abstract
We propose a method to improve the computational and memory efficiency of numerical solvers for the nonequilibrium Dyson equation in the Keldysh formalism. It is based on the empirical observation that the nonequilibrium Green's functions and self energies arising in many problems of physical interest, discretized as matrices, have low rank off-diagonal blocks, and can therefore be compressed using a hierarchical low rank data structure. We describe an efficient algorithm to build this compressed representation on the fly during the course of time stepping, and use the representation to reduce the
cost of computing history integrals, which is the main computational
bottleneck. For systems with the hierarchical low rank property, our
method reduces the computational complexity of solving the
nonequilibrium Dyson equation from cubic to near quadratic, and the
memory complexity from quadratic to near linear. We demonstrate the full
solver for the Falicov-Kimball model exposed to a rapid ramp and
Floquet driving of system parameters, and are able to
increase feasible propagation times substantially. We present examples with
262 144 time steps, which would require approximately five months
of computing time and 2.2 TB of memory using the direct time stepping method,
but can be completed in just over a day on a laptop with
less than 4 GB of memory using our method.
We also confirm the hierarchical low
rank property for the driven Hubbard model in the weak coupling regime
within the GW approximation, and in the strong coupling regime
within dynamical mean-field theory.
Funder
Javna Agencija za Raziskovalno Dejavnost RS
Simons Foundation
Subject
General Physics and Astronomy
Cited by
17 articles.
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