  We study theoretically the localization properties of two distinct
one-dimensional quasiperiodic lattice models with a single-particle mobility
edge (SPME) separating extended and localized states in the energy spectrum.
The first one is the familiar Soukoulis-Economou trichromatic potential model
with two incommensurate potentials, and the second is a system consisting of
two coupled 1D Aubry-Andre chains each containing one incommensurate potential.
We show that as a function of the Hamiltonian model parameters, both models
have a wide single-particle intermediate phase (SPIP), defined as the regime
where localized and extended single-particle states coexist in the spectrum,
leading to a behavior intermediate between purely extended or purely localized
when the system is dynamically quenched from a generic initial state. Our
results thus suggest that both systems could serve as interesting experimental
platforms for studying the interplay between localized and extended states, and
may provide insight into the role of the coupling of small baths to localized
systems. We also calculate the Lyapunov (or localization) exponent for several
incommensurate 1D models exhibiting SPME, finding that such localization
critical exponents for quasiperiodic potential induced localization are
nonuniversal and depend on the microscopic details of the Hamiltonian.
