Course Syllabus
pdf file
Background material readings
Reading 1 : More is different. P. W. Anderson(1972). Science, 177(4047), 393-396.
Reading 2 : On the nature of research in condensed state physics. A. J. Leggett(1992). Foundations of Physics, 22, 221-233.
Reading 3 : Electronic Society. C. Wu(2022). 物理, 2022, 51(1): 53-58.
Reading 4 : Richard Feynman and the history of superconductivity. D. Goodstein, J. Goodstein(2000). Physics in Perspective, 2, 30-47.
Lecture notes
Part I: Preparation
1. Reviews
Lecture -1 : Single-particle physics
Lecture 0 : The 2nd quantization method
Part II: Many-body physics without field theory
1. Elementary topics
Lecture 1 : Hartree-Fock approximation
Lecture 2 : Density functional theory
Lecture 3 : Hubbard model, Heisenberg model, spin wave
2. Interacting fermions
Lecture 4 : Interacting electron gas– Lindhard response, plasmon, screening
Lecture 5 : Fermi liquid theory (I)– quasi-particles and Landau interaction parameters
Lecture 6 : Fermi liquid theory (II)– renormalization to physical properties
Lecture 7 : Fermi liquid theory (III)– the Boltzmann equation and zero sound
Lecture 8 : Electron phonon interaction in metals
3. Superconductivity
Lecture 9 : Phenomenology of superconductivity
Lecture 10 : Bardeen-Cooper-Schrieffer theory to superconductivity
Lecture 11 : Thermodynamic properties, McMillan formula, linear response and coherence factor
Lecture 12 : Ginzburg-Landau formalism, dirty superconductor
Lecture 13 : (TBA) Josephson effect
Lecture 14 : Unconventional superconductivity
Part III: Field theory description of many-body physics
1. Formalism development
Lecture 15 : Path integral for quantum mechanics
Lecture 16 : Operator formalism, response functions
Lecture 17 : Path integral for functional fields and fermions
Lecture 18 : Perturbation theory for fermions
2. Fermi liquid and superconductivity
Lecture 19 : RPA, correlation energy
Lecture 20 : Quasiparticle life time, Fermi surface
Lecture 21 : Spin waves in itinerant ferromagnets
Lecture 22 : Vertex functions, Ward identities
Lecture 23 : Luttinger theorem
Final projects
1. Plasmon
Project 1(a) : Pines' demon. Wikipedia.
Project 1(b) : Remarks on Bloch's method of sound waves applied to many-fermion problems. S. I. Tomonaga(1950). Progress of Theoretical Physics, 5(4), 544-569.
2. New progress in Fermi liquid theory
Project 2(a) : Fermi liquid instabilities in the spin channel. C. Wu, K. Sun, E. Fradkin, et al(2007). Physical Review B, 75(11), 115103.
Project 2(b) : Dynamic generation of spin-orbit coupling. C. Wu, S. C. Zhang(2004). Physical review letters, 93(3), 036403.
Project 2(c) : Emerging research landscape of altermagnetism. L. Šmejkal, J. Sinova, T. Jungwirth(2022). Physical Review X, 12(4), 040501.
Project 2(d) : A parity-breaking electronic nematic phase transition in the spin-orbit coupled metal Cd2Re2O7. J. W. Harter, Z. Y. Zhao, J. Q. Yan, et al(2017). Science, 356(6335), 295-299.
3. Spin-orbit coupling
Project 3(a) : Spin-orbit coupled Fermi liquid theory of ultracold magnetic dipolar fermions. Y. Li, C. Wu(2012). Physical Review B, 85(20), 205126.
Project 3(b) : The J-triplet Cooper pairing with magnetic dipolar interactions. Y. Li, C. Wu(2012). Scientific reports, 2(1), 392.
4. Magnetic exchanges
Project 4(a) : Exchange in magnetic insulators. P. W. Anderson(2005). Career In Theoretical Physics, A (Vol. 35). World Scientific.
Project 4(b) : The Jahn-Teller effect and magnetism: transition metal compounds. K. I. Kugel, D. I. Khomskiĭ(1982). Soviet Physics Uspekhi, 25(4), 231.
Project 4(c) : Symmetry and the macroscopic dynamics of magnetic materials. A. F. Andreev, V. I. Marchenko(1980). Soviet Physics Uspekhi, 23(1), 21.
Project 4(d) : Multiflavor Mott insulators in quantum materials and ultracold atoms. G. V. Chen, C. Wu(2024). npj Quantum Materials, 9(1), 1.
5. Density functional theory
Project 5(a) : Density functional theory for field theorists I. T. Banks(2015). arXiv preprint arXiv:1503.02925.
Project 5(b) : A bird's-eye view of density functional theory. K. Capelle(2006). Brazilian journal of physics, 36, 1318-1343.
6. Schwinger boson method to Heisenberg model
Project 6(a) : Functional integral theories of low-dimensional quantum Heisenberg models. D. P. Arovas, A. Auerbach(1988). Physical Review B, 38(1), 316.
Project 6(b) : Schwinger-boson mean-field theory of the Heisenberg ferrimagnetic spin chain. C. Wu, B. Chen, X. Dai, et al(1999). Physical Review B, 60(2), 1057.
7. Itinerant ferromagnetism
Project 7(a) : Sign-problem-free quantum monte carlo study on thermodynamic properties and magnetic phase transitions in orbital-active itinerant ferromagnets. S. Xu,Y. Li, C. Wu(2015). Physical Review X, 5(2), 021032.
Project 7(b) : Exact results for itinerant ferromagnetism in multiorbital systems on square and cubic lattices. Y. Li, E. H. Lieb, C. Wu(2014). Physical Review Letters, 112(21), 217201.
8. Macroscopic Parity Nonconservation
Project 8(a) : Macroscopic Parity Nonconservation Due to Neutral Currents? Leggett, A. J. (1977). Physical Review Letters, 39(10), 587.
Back to home
Last modified: July 2, 2022.
Lecture notes
Part I: Preparation
1. Reviews
Lecture -1 : Single-particle physics
Lecture 0 : The 2nd quantization method
Part II: Many-body physics without field theory
1. Elementary topics
Lecture 1 : Hartree-Fock approximation
Lecture 2 : Density functional theory
Lecture 3 : Hubbard model, Heisenberg model, spin wave
2. Interacting fermions
Lecture 4 : Interacting electron gas– Lindhard response, plasmon, screening
Lecture 5 : Fermi liquid theory (I)– quasi-particles and Landau interaction parameters
Lecture 6 : Fermi liquid theory (II)– renormalization to physical properties
Lecture 7 : Fermi liquid theory (III)– the Boltzmann equation and zero sound
Lecture 8 : Electron phonon interaction in metals
3. Superconductivity
Lecture 9 : Phenomenology of superconductivity
Lecture 10 : Bardeen-Cooper-Schrieffer theory to superconductivity
Lecture 11 : Thermodynamic properties, McMillan formula, linear response and coherence factor
Lecture 12 : Ginzburg-Landau formalism, dirty superconductor
Lecture 13 : (TBA) Josephson effect
Lecture 14 : Unconventional superconductivity
Part III: Field theory description of many-body physics
1. Formalism development
Lecture 15 : Path integral for quantum mechanics
Lecture 16 : Operator formalism, response functions
Lecture 17 : Path integral for functional fields and fermions
Lecture 18 : Perturbation theory for fermions
2. Fermi liquid and superconductivity
Lecture 19 : RPA, correlation energy
Lecture 20 : Quasiparticle life time, Fermi surface
Lecture 21 : Spin waves in itinerant ferromagnets
Lecture 22 : Vertex functions, Ward identities
Lecture 23 : Luttinger theorem
Final projects
1. Plasmon
Project 1(a) : Pines' demon. Wikipedia.
Project 1(b) : Remarks on Bloch's method of sound waves applied to many-fermion problems. S. I. Tomonaga(1950). Progress of Theoretical Physics, 5(4), 544-569.
2. New progress in Fermi liquid theory
Project 2(a) : Fermi liquid instabilities in the spin channel. C. Wu, K. Sun, E. Fradkin, et al(2007). Physical Review B, 75(11), 115103.
Project 2(b) : Dynamic generation of spin-orbit coupling. C. Wu, S. C. Zhang(2004). Physical review letters, 93(3), 036403.
Project 2(c) : Emerging research landscape of altermagnetism. L. Šmejkal, J. Sinova, T. Jungwirth(2022). Physical Review X, 12(4), 040501.
Project 2(d) : A parity-breaking electronic nematic phase transition in the spin-orbit coupled metal Cd2Re2O7. J. W. Harter, Z. Y. Zhao, J. Q. Yan, et al(2017). Science, 356(6335), 295-299.
3. Spin-orbit coupling
Project 3(a) : Spin-orbit coupled Fermi liquid theory of ultracold magnetic dipolar fermions. Y. Li, C. Wu(2012). Physical Review B, 85(20), 205126.
Project 3(b) : The J-triplet Cooper pairing with magnetic dipolar interactions. Y. Li, C. Wu(2012). Scientific reports, 2(1), 392.
4. Magnetic exchanges
Project 4(a) : Exchange in magnetic insulators. P. W. Anderson(2005). Career In Theoretical Physics, A (Vol. 35). World Scientific.
Project 4(b) : The Jahn-Teller effect and magnetism: transition metal compounds. K. I. Kugel, D. I. Khomskiĭ(1982). Soviet Physics Uspekhi, 25(4), 231.
Project 4(c) : Symmetry and the macroscopic dynamics of magnetic materials. A. F. Andreev, V. I. Marchenko(1980). Soviet Physics Uspekhi, 23(1), 21.
Project 4(d) : Multiflavor Mott insulators in quantum materials and ultracold atoms. G. V. Chen, C. Wu(2024). npj Quantum Materials, 9(1), 1.
5. Density functional theory
Project 5(a) : Density functional theory for field theorists I. T. Banks(2015). arXiv preprint arXiv:1503.02925.
Project 5(b) : A bird's-eye view of density functional theory. K. Capelle(2006). Brazilian journal of physics, 36, 1318-1343.
6. Schwinger boson method to Heisenberg model
Project 6(a) : Functional integral theories of low-dimensional quantum Heisenberg models. D. P. Arovas, A. Auerbach(1988). Physical Review B, 38(1), 316.
Project 6(b) : Schwinger-boson mean-field theory of the Heisenberg ferrimagnetic spin chain. C. Wu, B. Chen, X. Dai, et al(1999). Physical Review B, 60(2), 1057.
7. Itinerant ferromagnetism
Project 7(a) : Sign-problem-free quantum monte carlo study on thermodynamic properties and magnetic phase transitions in orbital-active itinerant ferromagnets. S. Xu,Y. Li, C. Wu(2015). Physical Review X, 5(2), 021032.
Project 7(b) : Exact results for itinerant ferromagnetism in multiorbital systems on square and cubic lattices. Y. Li, E. H. Lieb, C. Wu(2014). Physical Review Letters, 112(21), 217201.
8. Macroscopic Parity Nonconservation
Project 8(a) : Macroscopic Parity Nonconservation Due to Neutral Currents? Leggett, A. J. (1977). Physical Review Letters, 39(10), 587.
Back to home
Last modified: July 2, 2022.
1. Reviews
1. Elementary topics
2. Interacting fermions
3. Superconductivity
1. Formalism development
2. Fermi liquid and superconductivity
Final projects
1. Plasmon
Project 1(a) : Pines' demon. Wikipedia.
Project 1(b) : Remarks on Bloch's method of sound waves applied to many-fermion problems. S. I. Tomonaga(1950). Progress of Theoretical Physics, 5(4), 544-569.
2. New progress in Fermi liquid theory
Project 2(a) : Fermi liquid instabilities in the spin channel. C. Wu, K. Sun, E. Fradkin, et al(2007). Physical Review B, 75(11), 115103.
Project 2(b) : Dynamic generation of spin-orbit coupling. C. Wu, S. C. Zhang(2004). Physical review letters, 93(3), 036403.
Project 2(c) : Emerging research landscape of altermagnetism. L. Šmejkal, J. Sinova, T. Jungwirth(2022). Physical Review X, 12(4), 040501.
Project 2(d) : A parity-breaking electronic nematic phase transition in the spin-orbit coupled metal Cd2Re2O7. J. W. Harter, Z. Y. Zhao, J. Q. Yan, et al(2017). Science, 356(6335), 295-299.
3. Spin-orbit coupling
Project 3(a) : Spin-orbit coupled Fermi liquid theory of ultracold magnetic dipolar fermions. Y. Li, C. Wu(2012). Physical Review B, 85(20), 205126.
Project 3(b) : The J-triplet Cooper pairing with magnetic dipolar interactions. Y. Li, C. Wu(2012). Scientific reports, 2(1), 392.
4. Magnetic exchanges
Project 4(a) : Exchange in magnetic insulators. P. W. Anderson(2005). Career In Theoretical Physics, A (Vol. 35). World Scientific.
Project 4(b) : The Jahn-Teller effect and magnetism: transition metal compounds. K. I. Kugel, D. I. Khomskiĭ(1982). Soviet Physics Uspekhi, 25(4), 231.
Project 4(c) : Symmetry and the macroscopic dynamics of magnetic materials. A. F. Andreev, V. I. Marchenko(1980). Soviet Physics Uspekhi, 23(1), 21.
Project 4(d) : Multiflavor Mott insulators in quantum materials and ultracold atoms. G. V. Chen, C. Wu(2024). npj Quantum Materials, 9(1), 1.
5. Density functional theory
Project 5(a) : Density functional theory for field theorists I. T. Banks(2015). arXiv preprint arXiv:1503.02925.
Project 5(b) : A bird's-eye view of density functional theory. K. Capelle(2006). Brazilian journal of physics, 36, 1318-1343.
6. Schwinger boson method to Heisenberg model
Project 6(a) : Functional integral theories of low-dimensional quantum Heisenberg models. D. P. Arovas, A. Auerbach(1988). Physical Review B, 38(1), 316.
Project 6(b) : Schwinger-boson mean-field theory of the Heisenberg ferrimagnetic spin chain. C. Wu, B. Chen, X. Dai, et al(1999). Physical Review B, 60(2), 1057.
7. Itinerant ferromagnetism
Project 7(a) : Sign-problem-free quantum monte carlo study on thermodynamic properties and magnetic phase transitions in orbital-active itinerant ferromagnets. S. Xu,Y. Li, C. Wu(2015). Physical Review X, 5(2), 021032.
Project 7(b) : Exact results for itinerant ferromagnetism in multiorbital systems on square and cubic lattices. Y. Li, E. H. Lieb, C. Wu(2014). Physical Review Letters, 112(21), 217201.
8. Macroscopic Parity Nonconservation
Project 8(a) : Macroscopic Parity Nonconservation Due to Neutral Currents? Leggett, A. J. (1977). Physical Review Letters, 39(10), 587.
1. Plasmon
2. New progress in Fermi liquid theory
3. Spin-orbit coupling
4. Magnetic exchanges
5. Density functional theory
6. Schwinger boson method to Heisenberg model
7. Itinerant ferromagnetism
8. Macroscopic Parity Nonconservation