(TUTH 10:30am -11:50pm, Mayer Hall Addition 4681) Course Syllabus pdf file

Lecture notes

1D physics -- integrable models, theta term, and bosonization

Lecture 1 : Bethe Ansatz (I) -- 2 magons, Bethe Ansatz equation, string states (bound states)

Further reading : Experimental observation of (many-body) Bethe string excitations

Lecture 2 : Bethe Ansatz (II) -- Many-magon states, factorization of scattering amplitude

Lecture 3 : Bethe Ansatz (III) -- Spin-1/2 antiferromagnetic spin chain, ground state energy, and spinon excitations

Further reading : Quantum dynamics of spin chain

Supplemental Material : Bethe Ansatz for 1D bosons with delta-interaction

Supplemental Material : Bethe Ansatz for 1D fermions -- Yang-Baxter equation

Lecture 4 : Spin coherenent state path integral

Lecture 5 : Renormalization group for the classic non-linear sigma model

Lecture 6 : Theta term, Haldane conjecture, AKLT and string order

Lecture 7 : 2D Ising model, Quantum Ising chain, Jordan-Wigner transformation, Kramers-Wannier duality

Supplemental Material : Correlation function of Ising model

Lecture 8 : Bosonization identity, operator product expansion, correlation functions

Further reading Constructive theory of bosonization

Lecture 9 : Luttinger liquid (I) (spinless) -- Luttinger model, Anomalous scaling dimension

Further readking Field theoretical version of bosonization

Lecture 10 : Luttinger liquid (II) (spinless) -- cosine terms, Sine-Gordon theory, CDW order

Supplemental Material (TBA) : KT transition, Coulomb gas, dielectric renormalization

Supplemental Material (TBA) : Introduction to conformal field theory

Supplemental Material : Helical Luttinger liquid theory

Lecture 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 orders

Further reading Baryon type ordering in 1D 4-component Fermi systems

2. Lattice gauge theory

Lecture 12 : Ising gauge theory

Lecture 13 : (TBA) Matter field, Fradkin-Shenker theorem

Lecture 14 : (TBA) 2D compact QED

Lecture 15 : (TBA) Application: quantum dimer model

3. Renormalization group for fermions

Lecture 16 : (TBA) Kondo problem, the poor-man scaling, spin-boson model

Lecture 17 : (TBA) Fermi liquid theory revisited from the RG perspective

Lecture 18 : (TBA) Hertz-Millis theory for the itinerant ferromagnetic criticality

Lecture 19 : (TBA) disordered electrons, scaling, non-linear sigma model


Howework assignment

Final project

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Last modified: Jan 7, 2010.