  The nonequilibrium Green's function formalism provides a versatile and
powerful framework for numerical studies of nonequilibrium phenomena in
correlated many-body systems. For calculations starting from an equilibrium
initial state, a standard approach consists of discretizing the Kadanoff-Baym
contour and implementing a causal time-stepping scheme in which the self-energy
of the system plays the role of a memory kernel. This approach becomes
computationally expensive at long times, because of the convolution integrals
and the large amount of computer memory needed to store the Green's functions.
A recent idea for the compression of nonequilibrium Green's functions is the
quantics tensor train representation. Here, we explore this approach by
implementing equilibrium and nonequilibrium simulations of the two-dimensional
Hubbard model with a second-order weak-coupling approximation to the
self-energy. We show that calculations with compressed two-time functions are
possible without any loss of accuracy, and that the quantics tensor train
implementation shows a much improved scaling of the computational effort and
memory demand with the length of the time contour.
