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Equilibrium Quantum Lattice SystemsDaniel Ueltschi (University of Warwick)
Tentative list of topics covered in the class:
1. Spin systems
Hilbert spaces, spin operators, symmetries, hamiltonians.
Finite-volume Gibbs states. Correlation functions.
Thermodynamic limit of the free energy.
2. Two results for quantum spins
o No long-range order in two dimensions, in systems with continuous symmetry.
o Long-range order in dimensions three and higher.
3. Fermionic and bosonic systems
Fock space, creation and annihilation operators. Bose-Einstein condensation.
Hubbard model.
4. Infinite-volume Gibbs states
Tangent functionals to the free energy. KMS condition.
Extremal state decomposition.
5. Probabilistic representations of quantum lattice systems
Feynman-Kac representation of Bose and spin systems.
Loop representations. Poisson-Dirichlet conjecture.