Condensed Matter

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

Z2 quantum lattice gauge theory, the toric code.

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.

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

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

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

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

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