Quantum Criticality and High-Temperature Superconductivity

Explore quantum criticality and high-temperature superconductivity through this comprehensive 8-hour lecture series delivered by K. Efetov as part of the 2013 Blaise Pascal Lectures. Begin with foundational concepts including Landau theory of phase transitions and fluctuations, then progress through classical criticality and divergences. Examine Josephson junctions and their role in quantum criticality before delving into Lagrangian formalism with imaginary time and phase diagrams. Investigate antiferromagnetic states and phase transitions in cuprates, followed by detailed analysis of the spin fermion model. Study ladder diagrams and mean field approximations within the spin fermion framework, then advance to fluctuations around mean field theory and sigma models. Conclude with renormalization group analysis, experimental comparisons, and future research directions in the field of quantum many-body systems and unconventional superconductivity.

Syllabus

K. Efetov 01 - Landau theory of phase transitions. Fluctuations.
K. Efetov 02 - Classical criticality and divergences.
K. Efetov 03 - Josephson junctions and quantum criticality.
K. Efetov 04 - Lagrangian formalism with an imaginary time. Phase diagram.
K. Efetov 05 - Antiferromagnetic states and phase transitions in Cuprates.
K. Efetov 06 - The spin fermion model.
K. Efetov 07 - Ladder diagrams in the spin fermion model
K. Efetov 08 - Mean field approximation in the spin fermion model
K. Efetov 09 - Fluctuations around the mean field. Sigma model.
K. Efetov 10 - RG analysis. Comparison with experiments. Outlook.