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[Print style]

Seminar on Spin Models", SS 2013

Spin models are a class of physical theories with a very precise mathematical formulation and interesting links to geometry, topology and representation theory. In our seminar we make an attempt to illuminate some of the typical physical problems arising in 1D and 2D spin models, ranging from the construction of spectrum and correlation functions to the analysis of excitations with non-abelian statistics.

Tentative schedule

The seminar takes place every Tuesday from 10:00h to 11:30h (plus x) in the seminar room in the container in front of the physics institutes. Lecture notes are available on request.
(Compact schedule in pdf format)

Date

Speaker

Title and literature

9.4.2013

T.Quella

Overview Talk: What are spin models?

Suggested literature:

  • R.J.Baxter: Exactly solved models in statistical mechanics

16.4.2013

D.Wieczorek

The Theorem of Lieb-Schultz-Mattis and Haldane’s Conjecture

Original literature:

23.4.2013

M.Zirnbauer

From network models to spin models

30.4.2013

P.Littelmann

The Yang-Baxter equation and its relation to integrable spin/vertex models: Transfer matrices, conserved quantities, partition function, examples

07.5.2013

T.Quella

Bethe ansatz for the ferromagnetic Heisenberg spin chain: Spectrum and correlation functions

14.5.2013

R.Bondesan

Spin chains from the Temperley-Lieb algebra

21.5.2013

No seminar

Possibly informal meeting

28.5.2013

D.Kus

The quantum group SUq(2) and its representations (incl. relation to the Yang-Baxter equation), peculiarities at roots of unity

4.6.2013

A.Alldridge

Abstract theory of the Yang-Baxter equation: Hopf algebras, universal R-matrix

11.6.2013

J.Peschutter

The Haldane-Shastry model: Long range interactions, groundstate wavefunction, excited states, Yangian symmetry

18.6.2013

T.Quella

The AKLT model: Construction of the Hamiltonian, the ground state and its uniqueness, edge modes, correlation functions, entanglement

25.6.2013

K.Duivenvoorden

Topological phases in 1D spin chains: Role of projective representations, central extensions and group cohomology

2.7.2013

I.Burban

The Drinfeld double [of a finite group] (mainly as an example leading to a tensor category and/or to a solution of the Yang-Baxter equation, link to universal R matrix)

9.7.2013

L.Galinat

Introduction to Tensor Categories

16.7.2013

S.Trebst

Topological phases in 2D: Quantum double models, anyonic statistics and topological quantum computation