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

TL;DR

This paper investigates how Parisi replica symmetry breaking affects elementary excitations in fermionic spin glasses, revealing exact solutions and implications for conductivity and neural network analogies.

Contribution

It provides exact solutions for the density of states in fermionic spin glasses with RPSB and introduces a new dynamical Parisi solution at infinite breaking levels.

Findings

RPSB significantly impacts fermionic excitations and conductivity.

Exact density of states obtained for K=1 RPSB at zero temperature.

Similarity observed between spin glass behavior and neural network problems.

Abstract

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=\infty. 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.