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:¶
Homework Assignments : 45%
Midterm Examination(Project proposal): 25%
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¶
Chaikin and Lubensky, Principles of Condensed Matter Physics
Piers Coleman, Introduction to Many-Body Physics
Xiao-Gang Wen, Quantum Field Theory of Many-Body Systems
Steven M. Girvin and Kun Yang, Modern Condensed Matter Physics
Auerbach, Interacting Electrons and Quantum Magnetism
Subir Sachdev, Quantum Phase Transitions
N. W. Ashcroft and N. D. Mermin, Solid State Physics
Eduardo Fradkin, Quantum Field Theory: An Integrated Approach
Alexander Altland and Ben Simons, Condensed Matter Field Theory
Philip Phillips, Advanced Solid State Physics
Anthony J. Leggett, Quantum Liquids
Selected contemporary review articles and research papers
Outline of the course¶
Concept of emergence
Basic tools for many-body theory
Single particle physics
Concept of quasi-particles
Quantum insulators
Entanglement and quantum matter
Tensor network
Quantum ergodicity
Course plan (2026-Fall, to be updated)¶
Introduction: Emergence and Quantum Many-Body Systems
Second Quantization and Collective Excitations
Tight-Binding Models and Bloch Theorem
Band Theory and Fermi Surfaces
Berry Phase and Topological Band Structures
Interacting Fermions and Response Functions
Landau Fermi Liquid Theory
Symmetry Breaking and Collective Modes
Renormalization Group and Universality
Path Integral Formulation
Green’s Functions and Spectral Representation
Diagrammatics and Linear Response Theory
Quantum Entanglement and Tensor-Network Concepts
Topological Order and Emergent Gauge Theory
ETH, Quantum Thermalization, and Many-Body Localization
Frontier Topics and Student Presentations