  We show that fermion systems with random interactions lead to strong coupling
of glassy order and fermionic correlations, which culminates in the
implementation of Parisi replica permutation symmetry breaking (RPSB) in their
T=0 quantum field theories. Precursor effects below fermionic AT-lines become
stronger as the temperature decreases and play a crucial role within the entire
low T regime. The Parisi ultrametric structure is shown to determine low energy
excitations and the dynamic behaviour of fermionic correlations for large
times, which is predicted to affect transport properties in metallic (and
superconducting) spin glasses. Thus we reveal quantum dynamical fingerprints of
the Parisi scheme. These effects, being strongest as T->0, are contrasted with
quantum spin glass transitions at T=0 displaying only small RPSB corrections at
low T. RPSB-effects moreover appear to influence the loci of the ground state
transitions at O(T^0) and hence the phase diagrams. We derive a new
representation of the T=0 Green's function which leads to a map of the
fermionic (insulating) spin glass solution to the local limit solution of a
Hubbard model with a random repulsive interaction. We obtain the distribution
of the Hubbard interaction fluctuation and its dependence on the order of RPSB.
A generalized mapping between metallic spin glass and random U Hubbard model is
conjectured. The new representation of the Green's function at T=0 is suggested
to be useful for generalizations to superconductors with spin glass phases.
