Jason Kaye (Flatiron Institute, USA) and Denis Golež (IJS and FMF UL): Compressing nonequilibrium evolution in quantum many-body systems

The nonequilibrium evolution in quantum many-body systems is accompanied by a growth in computational and memory complexity which prevents the exploration of long-time dynamics. We will present a numerical method based on nonequilibrium field theory, in which we tackle the complexity problem by an on-the-fly compression scheme. The algorithm relies on the empirical observation that nonequilibrium Green's functions often have a hierarchical low-rank structure, and are therefore highly compressible. Our method reduces the computational cost of the solution of the nonequilibrium Dyson equation from cubic to near quadratic, and the storage requirement from quadratic to near linear. We will confirm the compressibility structure for different excitation protocols in various models, including the Falicov-Kimball and Hubbard model. Two speakers will present the seminar to emphasize both the physics and applied mathematics aspects of the work, and to indicate opportunities for further collaboration between these two communities.