Quantum Phase Transitions
in
Interacting Disordered Electron Systems


D. Belitz
University of Oregon



I. Quantum Phase Transitions


II. A Model for Interacting Disordered Electrons


III. Metal-Insulator Transitions in Systems with Spin-Flip Mechanisms


IV. The Generic Universality Class


V. Summary and Conclusion


I. QUANTUM PHASE TRANSITIONS


Quantum phase transitions occur at T=0 as a function of some non-thermal control parameter.



Conductivity and dielectric susceptibility:

Infrared absorption coefficient:




II. A MODEL FOR INTERACTING DISORDERED ELECTRONS


1. Generalized Nonlinear Sigma Model



2. Universality Classes


III. METAL-INSULATOR TRANSITIONS IN SYSTEMS WITH SPIN-FLIP MECHANISMS


Loop expansion (= expansion in = d-2)


IV. THE GENERIC UNIVERSALITY CLASS


1. The Origin of the Myth: Low-Order RG



2. Perturbation Theory To All Orders



3. Solution of Integral Equations: Ferromagnetic Transition



4. Order Parameter Theory for the Magnetic Transition



5. Confirmation By Other Approaches



6. Metal-Insulator Transition


V. SUMMARY AND CONCLUSION