Magnetic instability and spin-glass order beyond the Anderson-Mott transition in interacting power-law random banded matrix fermions

TL;DR

This paper investigates how magnetic moments and spin-glass order emerge near the metal-insulator transition in a disordered fermion model, revealing a smooth evolution from metallic to insulating magnetic states due to interference effects.

Contribution

It demonstrates that interference effects enhance magnetic fluctuations and lead to spin-glass order beyond the Anderson-Mott transition in a power-law random banded matrix model.

Findings

Density of states and magnetic fluctuations increase approaching the MIT.

Local moments nucleate and grow continuously into the insulating phase.

Spin-glass order is identified in the insulator via overlap distribution.

Abstract

In the presence of quenched disorder, the interplay between local magnetic-moment formation and Anderson localization for electrons at a zero-temperature, metal-insulator transition (MIT) remains a long unresolved problem. Here, we study the emergence of these phenomena in a power-law random banded matrix model of spin-1/2 fermions with repulsive Hubbard interactions. Focusing on the regime of weak interactions, we perform both analytical field theory and numerical self-consistent Hartree-Fock calculations. We show that interference-mediated effects strongly enhance the density of states and magnetic fluctuations upon approaching the MIT from the metallic side. These are consistent with results due to Finkel'stein obtained four decades ago. Our numerics further show that local moments nucleate from typical states as we cross the MIT, with a density that grows continuously into the insulating phase. We identify spin-glass order in the insulator by computing the overlap distribution between converged Hartree-Fock mean-field moment profiles. Our results indicate that itinerant interference effects can morph smoothly into moment formation and magnetic frustration within a single model, revealing a common origin for these disparate phenomena.