PSI 2018/2019 - Condensed Matter Review (Hamma)

Research in quantum complexity and the emergence of irreversibility

Averages in the Hilbert space; entanglement typicality

Temporal fluctuations of observables; entanglement typicality

Equilibration and thermalization in quantum systems

The toric code: emergence of bosons and fermions; behaviour of the reduced system

The toric code: introduction; the toric code as a theory of strings

Phases and phases transitions in the Z_2 quantum lattice gauge theory

Classical lattice gauge theory; Elitzur's theorem; quantum lattice gauge theory

Clustering of correlations

Emergence of light cones; locality in non-relativistic quantum mechanics; Lieb-Robinson bounds

Geometry of the Hilbert space and quantum phase transitions; quantum geometric tensor; application to the quantum XY model; scaling behaviour

Discussion of whether symmetry can classify all possible states; distances between quantum states