  Disordered quantum systems undergoing a many-body localization (MBL)
transition fail to reach thermal equilibrium under their own dynamics.
Distinguishing between asymptotically localized or delocalized dynamics based
on numerical results is however nontrivial due to finite-size effects.
Numerical linked cluster expansions (NLCE) provide a means to tackle quantum
systems directly in the thermodynamic limit, but are challenging for models
without translational invariance. Here, we demonstrate that NLCE provide a
powerful tool to explore MBL by simulating quench dynamics in disordered
spin-$1/2$ two-leg ladders and Fermi-Hubbard chains. Combining NLCE with an
efficient real-time evolution of pure states, we obtain converged results for
the decay of the imbalance on long time scales and show that, especially for
intermediate disorder below the putative MBL transition, NLCE outperform direct
simulations of finite systems with open or periodic boundaries. Furthermore,
while spin is delocalized even in strongly disordered Hubbard chains with
frozen charge, we unveil that an additional tilted potential leads to a drastic
slowdown of the spin imbalance and nonergodic behavior on accessible times. Our
work sheds light on MBL in systems beyond the well-studied disordered
Heisenberg chain and emphasizes the usefulness of NLCE for this purpose.
