Dynamical CPA approach to an itinerant fermionic spin glass model

TL;DR

This paper develops a dynamical CPA method to analyze a fermionic spin glass model with hopping, deriving self-consistency equations and estimating the quantum critical point through numerical approximations.

Contribution

It introduces a dynamical CPA approach to a fermionic spin glass model with hopping, providing a new way to analyze quantum criticality in such systems.

Findings

Derived self-consistency equations for the model.

Implemented an approximation scheme for numerical solutions.

Estimated the quantum critical point location.

Abstract

We study a fermionic version of the Sherrington-Kirkpatrick model including nearest-neighbor hopping on a $\infty$-dimensional simple cubic lattices. The problem is reduced to one of free fermions moving in a dynamical effective random medium. By means of a CPA method we derive a set of self-consistency equations for the spin glass order parameter and for the Fourier components of the local spin susceptibility. In order to solve these equations numerically we employ an approximation scheme which restricts the dynamics to a feasible number of the leading Fourier components. From a sequence of systematically improved dynamical approximations we estimate the location of the quantum critical point.