Low-energy excitations in fermionic spin glasses: A quantum-dynamical image of Parisi symmetry breaking

We report large effects of Parisi replica permutation symmetry breaking (RPSB) on elementary excitations of fermionic systems with frustrated magnetic interactions. The electronic density of states is obtained exactly in the zero-temperature limit for (K = 1)-step RPSB together with exact relations for arbitrary breaking K, which lead to a new fermionic and dynamical Parisi solution at K = infinity. The Ward identity for charge conservation indicates RPSB effects on the conductivity in metallic quantum spin glasses. This implies that RPSB is essential for any fermionic system showing spin glass sections within its phase diagram. An astonishing similarity with a neural network problem is also observed.