: Quantum dynamics of spin chainSupplemental Material : Bethe Ansatz for 1D bosons withdelta-interactionSupplemental Material : Bethe Ansatz for 1D fermions -- Yang-Baxter equation Lecture 4 : Spin coherenent state path integralLecture 5 : Renormalization group for theclassic non-linear sigma modelLecture 6 : Theta term, Haldane conjecture, AKLT and string orderLecture 7 : 2D Ising model, Quantum Ising chain, Jordan-Wigner transformation, Kramers-Wannier dualitySupplemental Material : Correlation function of Ising model Lecture 8 : Bosonization identity,operator product expansion, correlation functionsFurther reading Constructive theory of bosonizationLecture 9 : Luttinger liquid (I) (spinless) -- Luttinger model, Anomalous scaling dimensionFurther readking Field theoretical version of bosonizationLecture 10 : Luttinger liquid (II) (spinless) -- cosine terms, Sine-Gordon theory, CDW orderSupplemental Material (TBA) : KT transition, Coulomb gas, dielectric renormalization Supplemental Material (TBA) : Introduction to conformal field theorySupplemental Material : Helical Luttinger liquid theoryLecture 11 : Luttinger liquid (III) (spinful) -- spin-charge separation, Mott gap and spin gap Supplemental Material : Kac-Moody algebra, more on OPE Supplemental Material : (TBA) Spectra properties of Luttinger liquid Further reading : Coupled Luttinger liquid -- competing ordersFurther reading Baryon type ordering in 1D 4-component Fermi systems 2. Lattice gauge theory
Lecture 12 : Ising gauge theoryLecture 13 : (TBA) Matter field, Fradkin-Shenker theorem Lecture 14 : (TBA) 2D compact QEDLecture 15 : (TBA) Application: quantum dimer model3. Renormalization group for fermions
Lecture 16 : (TBA) Kondo problem, the poor-man scaling, spin-bosonmodel Lecture 17 : (TBA) Fermi liquid theory revisited from the RG perspectiveLecture 18 : (TBA) Hertz-Millis theory for the itinerant ferromagnetic criticalityLecture 19 : (TBA) disordered electrons, scaling, non-linear sigma model Howework assignment
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