This course focuses on the field theory methods in condensed matter systems. We start with the principle of quantum field theory to describe the collective modes of solids, following the standard 1D and 2D Bosonization methods on interacting electrons, and introducing the concept of the renormalization group, topological quantum field theories, conformal field theories and gauge theories.
2020 spring we will do some online lectures [mandarine + english] due to the outbreak of the coronavirus.
IQHE
https://youtu.be/qjG-3byGsjY (Laughlin's argument and Chern number)
https://youtu.be/vLMqV-WUNQM (Kubo Formula and TKNN number)
https://youtu.be/_xWyET_840w (Fermion Path Integral and Chern-Simons Action)
Bosonization
https://youtu.be/1g82cuHOJs0 (particle-hole excitation and bosonic commutation relation.)
https://youtu.be/jNInVrhxaPs (Klein factor and fermion-boson mapping)
https://youtu.be/CVr62nqgv-s (Fermionic properties from bosonization)
https://youtu.be/84xfPbGXK-o (Spin-charge seperation and Umklapp term)
Landau Fermi liquids
https://youtu.be/COP1gvwXBos (Hydrodynamics and Landau parameters)
https://youtu.be/hnp_Iw7BLO8 (Zero sound and Bosonization of Fermi liquids)
https://youtu.be/jtFRevrYQ4k (Collective modes)
Path integral and Partition function
https://youtu.be/GCuDZfp7wq0 (Quantum Mechanics approach)
https://youtu.be/oA-o7bSnrvc (Quantum Field Theory approach)
Renormalizatoin Group
https://youtu.be/S1O33_vTjtk (Concept of RG)
https://youtu.be/5Z-9U4b5fsA (Real space RG in 1D and 2D Ising models)
https://youtu.be/x5XlLudqD7A (DMRG and phi 4)
https://youtu.be/atvHVe5uJF8 (phi 4 in d>4 and Gaussian fixed point)
https://youtu.be/kqEzlHMbafY (phi4 in d<4 and Wilson-Fisher fixed point)
https://youtu.be/meEBdgRFO9s (RG analysis of relativistic fermions in 1D)
https://youtu.be/BFHE5HRY6xU (RG analysis of 2D Fermi liquids)
Conformal field theories
https://youtu.be/V7zjZYTwCeM (conformal quantum mechanics)
https://youtu.be/F4kxYbP6J6A (conformal transformation and correlation functions)
https://youtu.be/UhRAOOdqJrU (2D conformal transformation and Virasoro algebra)
https://youtu.be/ZOkvp7znra0 (Stress energy tensor and trace anomaly)
Strongly correlated systems with fractionalization and emergent gauge fields
https://youtu.be/bRG5YBzoU-Q (fractionalization, emergent gauge theories and topological orders)
https://youtu.be/iyq20pyo-qY (Z2 gauge theory and Kitaev spin liquids)
Homework sets
Homework No.4 (2019)