Condensed Matter Quantum ManyBody Systems and Field Theory 2
Module PH7011
This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.
Basic Information
PH7011 is a semester module in English language at Master’s level which is offered in winter semester.
This Module is included in the following catalogues within the study programs in physics.
 Focus Area Theoretical Quantum Science & Technology in M.Sc. Quantum Science & Technology
If not stated otherwise for export to a nonphysics program the student workload is given in the following table.
Total workload  Contact hours  Credits (ECTS) 

270 h  90 h  9 CP 
Responsible coordinator of the module PH7011 is Jan von Delft.
Content, Learning Outcome and Preconditions
Content
This module develops advanced methods to study interacting quantum manyparticle systems in and out of equilibrium. The module starts with a short recapitulation of field theoretical fundamentals, in particular functional integral techniques. The next part of the module introduces the renormalization group as a central tool for understanding effective lowenergy properties of interacting quantum manyparticle systems. Topics include scaling, perturbative renormalization, RG flows and fixed points, as well as the Kondo effect and the superfluidMott insulator transition as examples. The module then covers fundamentals of lowdimensional systems (Luttinger liquids, bosonization) and the Keldysh technique to study manyparticle systems out of equilibrium. Final topics include instantons and nonperturbative techniques as well as optional topics, such as the quantum Hall effect (integer and fractional), ChernSimons theory, disorder in manyparticle systems, highTc superconductivity and quantum phase transitions.
Learning Outcome
After completing the Module the student is able to:

Explain the basic ideas of a renormalization group transformation.

Understand the concept of RG flows and RG fixed points.

Perform perturbative renormalization group computations.

Explain what the Kondo effect is.

Use bosonization to understand properties of lowdimensional quantum systems.

Explain how the Keldysh formalism is used to study nonequilibrium phenomena.

Explain what an instanton is.
Preconditions
Quantum ManyBody Systems and Field Theory I, or equivalent knowledge of second quantization, functional integrals, Green’s functions.
Courses, Learning and Teaching Methods and Literature
Learning and Teaching Methods
The module consists of a lecture series (4 SWS) and exercise classes (2 SWS), comprising two lecture sessions and one exercise session per week.
The main teaching material is presented on the blackboard or by beamer. Lectures are supplemented by weekly problem sets, deepening the understanding of core concepts through concrete calculations. Solutions to the problem sets are discussed in the exercise sessions.
Participation in the exercise classes is strongly recommended, since the exercises are aids for acquiring a deeper understanding of the core tools of condensed matter manybody physics and field theory and for practicing to solve typical exam problems.
Media
Power point and One Note presentations, blackboard.
Literature
Standard textbooks on manybody theory, e.g.:
• „Condensed Matter Field Theory“, A. Altland, B. Simons, Cambridge University Press
• „Scaling and Renormalization in Statistical Physics“, J. Cardy, Cambridge University Press
• "Field Theories of Condensed Matter Physics“, E. Fradkin, Cambridge University Press
• "Field Theory of NonEquilibrium Systems“, A. Kamenev, Cambridge University Press
• „Quantum Physics in One Dimension“, T. Giamarchi, Clarendon Press
Module Exam
Description of exams and course work
There will be a written exam of 180 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using conceptual questions and computational tasks.
For example an assignment in the exam might be:
 How do you perform a renormalization group transformation?
 What is the WilsonFisher fixed point?
 What are critical exponents and how do they relate to RG eigenvalues?
 How does the RG flow for the Kondo effect look like?
 Define the Keldysh contour.
 How are the different components of the Keldysh Green’s function related?
 Explain what the Luttinger parameter is.
 How does the bosonized electron density operator look like?
 Explain the phenomenon of spinchare separation.
Exam Repetition
The exam may be repeated at the end of the semester.