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

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.

v2: 25 pages, 21 figures; published version

References in corpus (12)

• Anderson Transitions
• Eigenfunction fractality and pseudogap state near superconductor-insulator transition
• Introduction to Random Matrices - Theory and Practice
• Topological protection, disorder, and interactions: Survival at the surface of 3D topological superconductors
• Pauli spin susceptibility of a strongly correlated two-dimensional electron liquid
• Observation of Spontaneous Ferromagnetism in a Two-Dimensional Electron System
• Spin-Droplet State of an Interacting 2D Electron System
• Magnetization of a strongly interacting two-dimensional electron system in perpendicular magnetic fields
• Levy flights and multifractality in quantum critical diffusion and in classical random walks on fractals
• Response theory of the ergodic many-body delocalized phase: Keldysh Finkel'stein sigma models and the 10-fold way
• Local moments and magnetic order in the two-dimensional Anderson-Mott transition
• Enhanced Amplitude for Superconductivity due to Spectrum-wide Wave Function Criticality in Quasiperiodic and Power-law Random Hopping Models