Beta-functions of non-linear $\sigma$-models for disordered and interacting electron systems

Abstract

We provide and study complete sets of one-loop renormalization group equations of several Finkel'stein non-linear $\sigma$-models, the effective field theories describing the diffusive quantum fluctuations in correlated disordered systems. We consider different cases according to the presence of certain symmetries induced by the original random Hamiltonians, and we show that, for interacting systems, the Cartan's classification of symmetry classes is not enough to uniquely determine their scaling behaviors.

16 pages, 4 figures, final version for the special issue "Many-Body Localization" in Annalen der Physik

References in corpus (7)

• Anderson Transitions
• Superconductor-insulator transitions: Phase diagram and magnetoresistance
• Metal-insulator transition from combined disorder and interaction effects in Hubbard-like electronic lattice models with random hopping
• Disordered d-wave superconductors with interactions
• Surface transport coefficients for three-dimensional topological superconductors
• Metal-insulator transition in Hubbard-like models with random hopping
• Two-loop renormalization of the Finkel'stein theory: The specific heat

Cited by in corpus (3)

• Interaction-induced metallicity in a two-dimensional disordered non-Fermi liquid
• Quantum Interference of Hydrodynamic Modes in a Dirty Marginal Fermi Liquid
• Magnetic instability and spin-glass order beyond the Anderson-Mott transition in interacting power-law random banded matrix fermions