PSI 2017/2018 - Condensed Matter (Hamma)

Equilibration and thermalization.

Equilibration in probability.

Loop structure, ground state and emergence of bosons and fermions in the toric code.

Z2 quantum lattice gauge theory, the toric code.

Phases and duality of Z2 quantum lattice gauge theory, Elitzur's theorem.

Quantum lattice gauge theory.

Clustering of correlations.

Applications of LR bounds: no signalling, truncation of time-evolved operators, spreading of correlations

Locality in quantum systems, Lieb-Robinson (LR) bounds.

Quantum geometric tensor, quantum phase transitions as "dramatic changes".

Statistical distance between quantum states, Fubini-Study metric on the Hilbert space.

Duality in the quantum Ising model, Jordan-Wigner transformation.