Thermodynamics of the disordered Hubbard model from numerical linked-cluster expansions*

The interplay of disorder and strong correlations in quantum many-body

systems remains an open question despite much progress that has been

made in recent years with ultracold atoms in optical lattices to better

understand phenomena such as many-body localization or the effect of

disorder on Mott metal-insulator transitions. Here we utilize the numerical

linked-cluster expansion technique, extended to deal with disordered

quantum lattice models in the thermodynamic limit, and study exact

thermodynamic properties of the disordered Fermi-Hubbard model on

the square lattice. We consider box distributions for the disorder in the

hopping amplitude as well as in the onsite energy or the interaction

strength and explore how the system properties evolve as the strength

of the disorder changes. We compare our results with those obtained

from determinant quantum Monte Carlo simulations on finite clusters
and discuss the potential applications of the results to experiments with

cold fermionic atoms on optical lattices.