**Abstract**

In the first sections, we bring into the present context some of our past contributions on the influence of quantum correlations on the formation of tightly bound solids. We discuss the effects of the overlap between neighbor orbitals in diverse situations of interest—involving both bulk and surface states—and call the reader's attention to an exact tight-binding calculation which allows gauging the errors introduced by the underlying hypotheses of the usual tight-binding approximation. We round up this part by reviewing a quantum Monte Carlo method specific for strongly correlated fermion systems. In the last section, we explore some nonequilibrium routes to (not necessarily tightly bound) solid state: we discuss spatiotemporal pattern formation in arrays of FitzHugh-Nagumo (FHN) neurons, akin to resonant crystal structures.

**Keywords:** quantum correlations, band structure, tight-binding approach, neighbor orbital overlap, fermion Monte Carlo, non-equilibrium pattern formation, spatiotemporal synchronization
