Syllabus for Physics 515: Solid State Physics II

Fall 2019

Books for reading list

• Economou, Green's Functions in Quantum Physics
• Freericks, Transport in multilayered nanostructures: the dynamical mean-field theory approach
• Kadanoff and Baym, Quantum statistical mechanics
• Ziman, Principles of the theory of solids
• Schrieffer, Theory of superconductivity
• Negele and Orland, Quantum many-particle systems

Lecture list

• Lecture 1: August 28, 2019. Contour integration and the theory of residues
• Optional reading: You may find chapters 2 and 4 of Marsden's Basic Complex Analysis as a good reference for this material.
• Lecture 2: August 30, 2019. Principal values and delta functions
• Lecture 3: September 3, 2019. Green's functions for single particle Hamiltonians I
• Reading: Economou, pp. 3-24.
• Lecture 4: September 4, 2019. Green's functions for single particle Hamiltonians II
• Reading: Economou, pp. 39-46.
• Last day for paper add/drop is September 6, 2019.
• Lecture 5: September 6, 2019. Tight-binding model in one, two, and three dimensions
• Reading: Economou, pp. 71-96.
• Lecture 6: September 10, 2019. Interacting Green's functions and the equation of motion
• Reading: Economou, pp. 199-214.
• Lecture 7: September 11, 2019. Analytic properties of Green's functions
• Reading: Economou, pp. 215-221.
• Lecture 8: September 13, 2019. Uses of the Green's functions
• Reading: Economou, pp. 221-229.
• Make-up day September 17, 2019.
• Lecture 9: September 18, 2019. Imaginary time Green's functions
• Reading: Kadanoff and Baym, pp. 1-9; Freericks, pp. 46-53.
• Lecture 10: September 20, 2019. Quasiparticles
• Reading: Economou, pp. 229-236.
• Lecture 11: September 24, 2019. Fermi liquid theory
• Reading: Economou, pp. 265-269.
• Lecture 12: September 25, 2019. Falicov-Kimball model
• Reading: Freericks, pp. 31-43.
• Lecture 13: September 27, 2019. Spinless atom in a time-dependent field
• Reading: Freericks, pp. 63-65.
• Lecture 14: October 1, 2019. Dynamical mean-field theory for the Falicov-Kimball model on the imaginary time/frequency axis
• Reading: Freericks, pp. 66-69.
• Lecture 15: October 2, 2019. Dynamical mean-field theory for the Falicov-Kimball model on the real axis
• Reading: Freericks, pp. 53-60.
• Lecture 16: October 4, 2019. Sum rules for the Green's functions and self-energies
• Reading: V. M. Turkowski and J. K. Freericks, Spectral moment sum rules for strongly correlated electrons in time-dependent electric fields, Phys. Rev. B 73 075108--1-15 (2006) 10.1103/PhysRevB.73.075108; Erratum, Phys. Rev. B 73, 209902(E)-1--1 (2006). 10.1103/PhysRevB.73.209902; V. M. Turkowski and J. K. Freericks, Nonequilibrium sum rules for the retarded self-energy of strongly correlated electrons, Phys. Rev. B 77, 205102-1--16 (2008). 10.1103/PhysRevB.77.205102. Erratum: Phys. Rev. B 82, 119904-1--3(E) (2010). 10.1103/PhysRevB.82.119904.
• Lecture 17: October 8, 2019. Kubo-Greenwood formula for linear response
• Reading: Freericks, pp. 80-84.
• Lecture 18: October 9, 2019. Charge conductivity
• Reading: Freericks, pp. 84-90.
• Lecture 19: October 11, 2019. Optical sum rule and differential equation
• Reading:Pierre F. Maldague, Phys. Rev. B 16, 2437 (1977) 10.1103/PhysRevB.16.2437.
• Lecture 20: October 15, 2019. Thermal transport
• Make-up Day October 16, 2019.
• Lecture 21: October 18, 2019. Jonson-Mahan theorem
• Lecture 22: October 22, 2019. Charge density waves I
• Reading: Freericks and Zlatic, Phys. Rev. B 58, 322 (1998) 10.1103/PhysRevB.58.322.
• Lecture 23: October 23, 2019. Charge density waves II
• Lecture 24: October 25, 2019. Ordered phase for the charge density wave
• Reading: Ling Chen, B. A. Jones, and J. K. Freericks, Charge-density-wave order parameter of the Falicov-Kimball model in infinite dimensions, Phys. Rev. B 68, 153102--1-4 (2003). 10.1103/PhysRevB.68.153102.
• Lecture 25: October 29, 2019. Introduction to superconductivity
• Reading:Ziman 11.1-11.3.
• Lecture 26: October 30, 2019. Cooper pair problem
• Reading: Bound Electron Pairs in a Degenerate Fermi Gas, Leon N. Cooper, Phys. Rev. 104, 1189 (1956) 10.1103/PhysRev.104.1189
• Lecture 27: November 1, 2019. Nambu Gor'kov formalism I
• Reading: Schrieffer, pp. 169-180.
• Lecture 28: November 5, 2019. Nambu Gor'kov formalism II
• Reading: Freericks, pp. 172-178.
• Lecture 29: November 6, 2019. Electron-phonon interaction/Migdal's theorem/Coulomb pseudopotential
• Lecture 30: November 8, 2019. Owens-Scalapino method for calculating the transition temperature
• Reading: S-state instabilities for retarded interactions, Owen, C.S.and Scalapino, D.J., Physica, 55, pp.691, (1971) 10.1016/0031-8914(71)90320-X.
• Lecture 31: November 12, 2019. Calculation of the tunneling conductance I
• Reading:Iterative analytic continuation of the electron self-energy to the real axis, F. Marsiglio, M. Schossmann, and J. P. Carbotte, Phys. Rev. B 37, 4965 (1988) 10.1103/PhysRevB.37.4965
• Lecture 32: November 13, 2019. Calculation of the tunneling conductance II
• Lecture 33: November 15, 2019. Bose coherent states
• Reading: Negele and Orland, pp. 1-25.
• Lecture 34: November 19, 2019. Fermi coherent states and Grassman variables
• Reading: Negele and Orland, pp. 25-33.
• Lecture 35: November 20, 2019. Gaussian integrals
• Reading: Negele and Orland, pp. 33-37.
• Last day to drop class is Nov. 21.
• Lecture 36: November 22, 2019. Particle in a time-dependent field in imaginary time
• Lecture 37: November 26, 2019. Particle in a time-dependent field in the Matsubara frequency representation
• Reading: J. K. Freericks and V. Zlatic', Exact dynamical mean field theory of the Falicov-Kimball model, Rev. Mod. Phys. 75, 1333--1382 (2003). 10.1103/RevModPhys.75.1333. (pages 1338-1341 only).
• No class, Happy Thanksgiving November 27, 2019
• Lecture 38: December 3, 2019. Coherent state functional integral and the Trotter formula
• Reading: Negele and Orland, pp. 63-74.
• Lecture 39: December 4, 2019. Hubbard-Stratanovitch transformation and the Hirsch-Fye algorithm
• Reading: Monte Carlo Method for Magnetic Impurities in Metals , J. E. Hirsch and R. M. Fye, Phys. Rev. Lett. 56, 2521 (1986) 10.1103/PhysRevLett.56.2521
• Makeup day December 6, 2019.