## Quantum Many-Body Physics

Lecturer: Michael Knap

Teaching Assistants: Annabelle Bohrdt, Johannes Feldmeier

**Fall Term**

Lectures: Mon/Wed 10:15-11:45, seminar room 3344

Practicals: Thu 16:00-17:30, seminar room 3344

This course provides a modern introduction to many-body physics. It covers basic theoretical methods and their application to various problems of condensed matter theory, such as the weakly interacting Bose gas, interacting electron gas, Fermi liquid theory, and superconductivity. Toward the end we will also branch out to study generic features in the far-from equilibrium quantum dynamics of strongly correlated quantum matter. Throughout the class relations between experiments and theory will be emphasized. This course will provide students the basic knowledge to follow state-of-the-art research in condensed matter physics and to be able to start their independent research project in that field.

A description of how this course will be graded can be found here.

**Outline:**

**Introduction**

(1.1) Mean-field theory [pdf]

(1.2) Landau theory of phase transitions [pdf]

(1.3) Quantum phases of matter [pdf]

(1.4) Second Quantization [pdf]

**Functional Field Integrals**

(2.1) Feynman's Path Integral in Single-particle QM [pdf]

(2.2) Bosonic and Fermionic Coherent States [pdf]

(2.3) Functional Field Integrals for the Partition Function [pdf]

**Weakly Interacting Bose Gas**

(3.1) Non-interacting bosons [pdf]

(3.2) Weakly interacting bosons [pdf]

(3.3) Consequences of a broken continuous symmetry [pdf]

(3.4) Superfluidity [pdf]

(3.5) Quantum disorder in one dimension [pdf]

(3.6) Thermal disorder and BKT transition [pdf]

**Linear Response Theory**

(4.1) Response functions [pdf]

(4.2) Fluctuation-dissipation relations [pdf]

(4.3) Analytic Properties of Correlation Functions [pdf]

(4.4) Sum rules [pdf]

**Fermi-Liquid Theory**

(5.1) The non-interacting Fermi gas [pdf]

(5.2) Quasi-particle excitations [pdf]

(5.3) Interacting fermion Greens functions and self energy [pdf]

(5.4) Landau's phenomenological approach [pdf]

(5.5) Dynamical properties of a Fermi liquid [pdf]

**The interacting electron gas**

(6.1) Hatree-Fock Approximation [pdf]

(6.2) Coulomb interactions [pdf]

**Superconductivity**

(7.1) The basic phenomenon [pdf]

(7.2) Anderson-Higgs Mechanism [pdf]

(7.3) Flux quantization and vortices in superconductors [pdf]

(7.4) BCS theory from functional field integrals [pdf]

(7.5) Microscopic derivation of the Ginzburg-Landau theory [pdf]

**Quantum Magnetism**

(8.1) Spin exchange [pdf]

(8.2) The Hubbard model and its descendents [pdf]

(8.3) AFM mean field theory at half filling [pdf]

(8.4) Spin-wave theory of Quantum magnets [pdf]

**Tutorials**

Problem Set 1 [pdf]

Problem Set 2 [pdf]

Problem Set 3 [pdf]

Problem Set 4 [pdf]

Problem Set 5 [pdf]

Problem Set 6 [pdf]

**List of Presentations** [pdf]