PSI 2017/2018 - Condensed Matter (Hamma)

Quantum phases and correlations, the thermodynamic limit, local quantum systems, quantum Ising model.

Local quantum systems, quantum evolution, definition of a phase.

Long-ranged order, quantum phases at zero temperature, quantum phases of the quantum Ising model.

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

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

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

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

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

Clustering of correlations.

Quantum lattice gauge theory.

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

Z2 quantum lattice gauge theory, the toric code.