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Lecture Notes
National Tsing Hua University

Syllabus

National Tsing Hua University

盡信書不如無書。 --孟子

道可道，非常道。 --老子

Keep throwing out the inessential until the problem becomes trivial. Then go back one step. -- Sam Edwards

Basic information

Lecture hours: Office hours: TA: TA office hours:

Evaluation:

  1. Homework Assignments : 45%

  2. Midterm Examination(Project proposal): 25%

  3. Final Examination(Presentation): 30%

Textbook

None

Course Description

This course introduces the fundamental concepts and modern paradigms of condensed matter theory from the perspective of emergence in quantum many-body systems. Starting from second quantization, collective excitations, band theory, and interacting fermions, the course develops the theoretical framework underlying quasiparticles, spontaneous symmetry breaking, topology, and universal low-energy behavior. Advanced topics including Berry phase, renormalization group, Green’s functions, quantum entanglement, tensor-network concepts, topological order, gauge theory, and quantum thermalization will also be introduced. Emphasis is placed not only on computational techniques, but also on the organizing principles that enable complex quantum matter to exhibit robust emergent phenomena. The course aims to provide graduate students with the conceptual and technical foundation necessary to engage with contemporary research in condensed matter physics and quantum many-body theory.

References

  1. Chaikin and Lubensky, Principles of Condensed Matter Physics, Chaikin et al. (1995)

  2. Piers Coleman, Introduction to Many-Body Physics, Coleman (2015)

  3. Xiao-Gang Wen, Quantum Field Theory of Many-Body Systems, Wen (2004)

  4. Steven M. Girvin and Kun Yang, Modern Condensed Matter Physics, Girvin & Yang (2019)

  5. Subir Sachdev, Quantum Phase Transitions, Sachdev (1999)

  6. N. W. Ashcroft and N. D. Mermin, Solid State Physics, Ashcroft & Mermin (1976)

  7. Eduardo Fradkin, Field theories of condensed matter physic, Fradkin (2013)

  8. Alexander Altland and Ben Simons, Condensed Matter Field Theory, Altland & Simons (2010)

  9. Philip Phillips, Advanced Solid State Physics, Phillips (2012)

  10. Anthony J. Leggett, Quantum Liquids, Leggett (2006)

  11. Selected contemporary review articles and research papers

Outline of the course

Course plan (2026-Fall, to be updated)

  1. Introduction: Emergence and Quantum Many-Body Systems

  2. Second Quantization and Collective Excitations

  3. Tight-Binding Models and Bloch Theorem

  4. Band Theory and Fermi Surfaces

  5. Berry Phase and Topological Band Structures

  6. Interacting Fermions and Response Functions

  7. Landau Fermi Liquid Theory

  8. Symmetry Breaking and Collective Modes

  9. Renormalization Group and Universality

  10. Path Integral Formulation

  11. Green’s Functions and Spectral Representation

  12. Diagrammatics and Linear Response Theory

  13. Quantum Entanglement and Tensor-Network Concepts

  14. Topological Order and Emergent Gauge Theory

  15. ETH, Quantum Thermalization, and Many-Body Localization

  16. Frontier Topics and Student Presentations

Acknowledgement:

References
  1. Chaikin, P. M., Lubensky, T. C., & Witten, T. A. (1995). Principles of condensed matter physics (Vol. 10). Cambridge university press Cambridge.
  2. Coleman, P. (2015). Introduction to many-body physics. Cambridge University Press.
  3. Wen, X.-G. (2004). Quantum field theory of many-body systems: From the origin of sound to an origin of light and electrons. Oxford university press.
  4. Girvin, S. M., & Yang, K. (2019). Modern condensed matter physics. Englisch (Cambridge University Pr., Cambridge New York, 2019).
  5. Sachdev, S. (1999). Quantum phase transitions. Physics World, 12(4), 33–38.
  6. Ashcroft, N. W., & Mermin, N. D. (1976). Solid state physics.
  7. Fradkin, E. (2013). Field theories of condensed matter physics. Cambridge University Press.
  8. Altland, A., & Simons, B. D. (2010). Condensed matter field theory. Cambridge university press.
  9. Phillips, P. (2012). Advanced solid state physics. Cambridge University Press.
  10. Leggett, A. J. (2006). Quantum liquids: Bose condensation and Cooper pairing in condensed-matter systems. Oxford university press.
Emergent phenomena
Week 1: Introduction and Emergence