Title: Time-dependent variational principle in matrix-product state manifolds: pitfalls and potential,
Abstract: We study the applicability of the time-dependent variational principle in
matrix product state manifolds for the long time description of quantum
interacting systems. By studying integrable and nonintegrable systems for which
the long time dynamics are known we demonstrate that convergence of long time
observables is subtle and needs to be examined carefully. Remarkably, for the
disordered nonintegrable system we consider the long time dynamics are in good
agreement with the rigorously obtained short time behavior and with previous
obtained numerically exact results, suggesting that at least in this case the
apparent convergence of this approach is reliable. Our study indicates that
while great care must be exercised in establishing the convergence of the
method, it may still be asymptotically accurate for a class of disordered
nonintegrable quantum systems.