  Quantum many-body systems out of equilibrium pose some of the most intriguing
questions in physics. Unfortunately, numerically keeping track of time
evolution of states under Hamiltonian dynamics constitutes a severe challenge
for all known methods. Prominently, tensor network methods are marred by an
entanglement blowup, which allows to simulate systems following global quenches
only to constant time. In this work, we present a scheme that allows to
significantly extend the simulation time for interacting fermionic or
equivalent spin systems. In the past when keeping track of evolution in
one-dimensional real space, the subspace parametrised by real-space matrix
product states satisfying area laws - often dubbed the "physical corner" of
Hilbert space - was chosen as variational set. In contrast, if the manifold
containing both tensor network states and fermionic mode transformations is
chosen, significantly longer times can be achieved. We argue and our results
suggest that in many cases it is genuine correlations between modes that is the
actual limiting factor: The system at hand is for intermediate times contained
in the "physical corner", but a different one than what is commonly assumed.

Statistical Mechanics;Strongly Correlated Electrons;Quantum Physics