We provide a pedagogical introduction to numerical linked-cluster expansions (NLCEs). We sketch the algorithm for generic Hamiltonians that only connect nearest-neighbor sites in a finite cluster with open boundary conditions. We then compare results for a specific model, the Heisenberg model, in each order of the NLCE with the ones for the finite cluster calculated directly by means of full exact diagonalization. We discuss how to reduce the computational cost of the NLCE calculations by taking into account symmetries and topologies of the linked clusters. Finally, we generalize the algorithm to the thermodynamic limit, and discuss several numerical resummation techniques that can be used to accelerate the convergence of the series.

We use thermalization indicators and numerical linked cluster expansions to probe the onset of many-body localization in a disordered one-dimensional hard-core boson model in the thermodynamic limit. We show that after equilibration following a quench from a delocalized state, the momentum distribution indicates a freezing of one-particle correlations at higher values than in thermal equilibrium. The position of the delocalization to localization transition, identified by the breakdown of thermalization with increasing disorder strength, is found to be consistent with the value from the level statistics obtained via full exact diagonalization of finite chains. Our results strongly support the existence of a many-body localized phase in the thermodynamic limit.

We use determinantal quantum Monte Carlo simulations and numerical linked-cluster expansions to study thermodynamic properties and short-range spin correlations of fermions in the honeycomb lattice. We find that, at half filling and finite temperatures, nearest-neighbor spin correlations can be stronger in this lattice than in the square lattice, even in regimes where the ground state in the former is a semimetal or a spin liquid. The honeycomb lattice also exhibits a more pronounced anomalous region in the double occupancy that leads to stronger adiabatic cooling than in the square lattice. We discuss the implications of these findings for optical lattice experiments.