  The majority of quantum simulators treat simplified one-band strongly
correlated models, whereas multiple bands are needed to describe materials with
intermediate correlation. We investigate the sensitivity of multiband quantum
simulators to: (1) the form of optical lattices (2) the interactions between
electron analogues. Since the kinetic energy terms of electron analogues in a
quantum simulator and electrons in a solid are identical, by examining both
periodic potential and interaction we explore the full problem of many-band
quantum simulators within the Born-Oppenheimer approximation. Density
functional calculations show that bandstructure is highly sensitive to the form
of optical lattice, and it is necessary to go beyond sinusoidal potentials to
ensure that the bands closest to the Fermi surface are similar to those in real
materials. Analysis of several electron analogue types finds that dressed
Rydberg atoms (DRAs) have promising interactions for multi band quantum
simulation. DRA properties can be chosen so that interaction matrices
approximate those in real systems and decoherence effects are controlled,
albeit with parameters at the edge of currently available technology. We
conclude that multiband quantum simulators implemented using the principles
established here could provide insight into the complex processes in real
materials.
