## Quantum Many-Body Physics

### Winter 2022/23

Lecturer: Michael Knap

Teaching Assistants: Ofir Arzi, Stefan Birnkammer, Philip Zechmann, Caterina Zerba

Lectures: Mon. 8:30-10:00, Wed. 16:00-17:30

(HS2 and HS3)

Tutorials: TBD

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.

The course will be offered this semester at the announced times and will be gien via Zoom. Further details will be sent by email to all participants registered in campus online. Please sign up online to be able to receive the latest information. The course material including lecture notes and excercises will be posted on moodle.

**Outline:**

**Introduction**

(1.1) Mean-field theory

(1.2) Landau theory of phase transitions

(1.3) Quantum phases of matter

(1.4) Second Quantization

**Functional Field Integrals**

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

(2.2) Bosonic and Fermionic Coherent States

(2.3) Functional Field Integrals for the Partition Function

**Weakly Interacting Bose Gas**

(3.1) Non-interacting bosons

(3.2) Weakly interacting bosons

(3.3) Consequences of a broken continuous symmetry

(3.4) Superfluidity

(3.5) Quantum disorder in one dimension

(3.6) Thermal disorder and BKT transition

**Linear Response Theory**

(4.1) Response functions

(4.2) Fluctuation-dissipation relations

(4.3) Analytic Properties of Correlation Functions

(4.4) Sum rules

**Fermi-Liquid Theory**

(5.1) The non-interacting Fermi gas

(5.2) Quasi-particle excitations

(5.3) Interacting fermion Greens functions and self energy

(5.4) Landau's phenomenological approach

(5.5) Dynamical properties of a Fermi liquid

**The interacting electron gas**

(6.1) Hartree-Fock Approximation

(6.2) Coulomb interactions

**Superconductivity**

(7.1) The basic phenomenon

(7.2) Anderson-Higgs Mechanism

(7.3) Flux quantization and vortices in superconductors

(7.4) BCS theory from functional field integrals

(7.5) Microscopic derivation of the Ginzburg-Landau theory

**Quantum Magnetism**

(8.1) Spin exchange

(8.2) The Hubbard model and its descendents

(8.3) AFM mean field theory at half filling

(8.4) Spin-wave theory of Quantum magnets

**Literature:**

P. Coleman, Introduction to Many-Body Physics

J. Negele & H. Orland, Quantum Many-particle Systems

A. Altland & B. Simons, Condensed Matter Field Theory

T. Giamachi, Quantum Physics in One Dimension

E. Fradkin, Field Theories of Condensed Matter Physics

X.-G. Wen, Quantum Field Theory of Many-Body Systems