  We propose and analyze a solid-state platform based on surface acoustic waves
(SAWs) for trapping, cooling and controlling (charged) particles, as well as
the simulation of quantum many-body systems. We develop a general theoretical
framework demonstrating the emergence of effective time-independent acoustic
trapping potentials for particles in two- or one-dimensional structures. As our
main example we discuss in detail the generation and applications of a
stationary, but movable acoustic pseudo-lattice (AL) with lattice parameters
that are reconfigurable in situ. We identify the relevant figures of merit,
discuss potential experimental platforms for a faithful implementation of such
an acoustic lattice, and provide estimates for typical system parameters. With
a projected lattice spacing on the scale of 100nm, this approach allows for
relatively large energy scales in the realization of fermionic Hubbard models,
with the ultimate prospect of entering the low temperature, strong interaction
regime. Experimental imperfections as well as read-out schemes are discussed.
