PSI 2018/2019 - Condensed Matter Review (Hamma)

Overview of the course; local quantum systems; the thermodynamic limit; graph theory; the quantum Ising model

Review of classical statistical mechanics; introduction to quantum phase transitions

Duality of the quantum Ising model; exact diagonalization of the quantum XY model using Jordan-Wigner transformation

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

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

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

Clustering of correlations

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

Phases and phases transitions in the Z_2 quantum lattice gauge theory

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

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