  We report the results of our theoretical studies of the time-reversal and
parity violating electric dipole moment (EDM) of $^{129}$Xe arising from the
nuclear Schiff moment (NSM) and the electron-nucleus tensor-pseudotensor (T-PT)
interaction based on the self-consistent and the normal relativistic
coupled-cluster methods. The important many-body effects are highlighted and
their contributions are explicitly presented. The uncertainties in the
calculations of the correlation and relativistic effects are determined by
estimating the contributions of the triples excitations, and the Breit
interaction respectively, which together amount to about 0.7% for the NSM and
0.2% for the T-PT interactions. The results of our present work in combination
with improved experimental limits for $^{129}$Xe EDM in the future would
tighten the constraints on the hadronic CP violating quantities, and this could
provide important insights into new physics beyond the Standard Model of
elementary particles.
