  We investigate spontaneous interlayer phase coherence and the occurrence of
the quantum Hall effect in triple-layer electron systems. Our work is based on
a simple tight-binding model that greatly facilitates calculations and whose
accuracy is verified by comparison with recent experiments. By calculating the
ground state in an unrestricted Hartree-Fock approximation and the
collective-mode spectrum in a time-dependent Hartree-Fock approximation, we
construct a phase diagram delimiting regions in the parameter space of the
model where the integer quantum Hall effect occurs in the absence of interlayer
tunneling.
