Quantum ManyBody Physics
Module PH2256
Module version of WS 2020/1 (current)
There are historic module descriptions of this module. A module description is valid until replaced by a newer one.
Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.
available module versions  

WS 2020/1  WS 2019/20  WS 2018/9  WS 2017/8 
Basic Information
PH2256 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.
 Theory courses for condensed matter physics
 Theory courses for Applied and Engineering Physics
 Focus Area Theoretical Quantum Science & Technology in M.Sc. Quantum Science & Technology
 Complementary catalogue of special courses for nuclear, particle, and astrophysics
 Complementary catalogue of special courses for Biophysics
 Specialization Modules in EliteMaster Program Theoretical and Mathematical Physics (TMP)
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) 

300 h  90 h  10 CP 
Responsible coordinator of the module PH2256 is Frank Pollmann.
Content, Learning Outcome and Preconditions
Content
This module provides an introduction into quantum manybody physics. We will cover basic quantum fieldtheoretical methods and their application to various manybody problems of condensed matter theory, such as Fermi and Luttinger liquids, superfluids and superconductors and quantum Hall fluids. This module will provide students with a basic knowledge for starting independent research in quantum condensed matter physics. The exercise classes will supplement the lectures with regular instructions and problem sets. The problem sets will help to understand and deepen the physical concepts presented in the lecture.
Outline:
 Introduction into quantum manybody problem:
emergence and collective behavior, quantum fields, second quantization  Path integral formulation of quantum field theory:
singleparticle quantum mechanics from the path integral, coherent states and functional integrals, partition function as a functional integral
 Linear response theory
response functions, fluctuationdissipation theorem, conductivity of Fermi gas  Fermi liquid theory:
Fermi liquid ground state, quasiparticles and their stability, collective modes, Landau damping, nonFermi liquids  Luttinger liquids:
pecularities of physics in one dimension, Luttinger model, basic of bosonization, correlation functions, relation to conformal field theories and twodimensional classical XY model  Superfluids and superconductors:
physical properties of superfluids and superconductors, BCS theory, phase stiffness, vortices, rotating superfluids, bosonvortex duality in two dimensions, BerezinskiiKosterlitzThouless transition, chiral superfluids and superconductors  Quantum Hall fluids:
basics of quantum Hall effect, flux attachment and ChernSimons theory, topological order and anyons in fractional quantum Hall fluids, abelian ChernSimons theory and the hierarchy of quanum Hall states, edge of quantum Hall fluids, nonabelian quantum Hall states, Dirac fermion duality
Learning Outcome
After successful completion of this module students will be able to
 apply field theory techniques in condensed matter physics
 use second quantization, coherent states, path integrals, linear resonse theory to solve manybody problems
 understand theoretical paradigms that are central in modern condensed matter physics
 have a working knowledge of the physics of Fermi liquids, onedimensional Luttinger liquids, superfluids and superconductors, quantum Hall liquids
Preconditions
No preconditions in addition to the requirements for the Master’s program in Physics.
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
Type  SWS  Title  Lecturer(s)  Dates  Links 

VO  4  Quantum ManyBody Physics  Knap, M. 
Mon, 10:00–12:00, PH 3344 Wed, 10:00–12:00, PH 3344 

UE  2  Quantum ManyBody Physics 
Bohrdt, A.
Feldmeier, J.
Responsible/Coordination: Knap, M. 
dates in groups 
Learning and Teaching Methods
The course consists of a lecture and exercise classes. The lecture is designed for the presentation of the subject, usually by blackboard presentation. The focus resides on theoretical foundations of the field, presentation of methods and simple, illustrative examples. Command of basic methods is deepened and practised through homework problems, which cover important aspects of the field. The homework problems should develop the analytic skills of the students and their ability to perform calculations. The homework problems are discussed in the exercises by the students themselves under the supervision of a tutor in order to develop the skills to explain a physics problem logically.
Media
In classroom lectures the content is presented on blackboard. Questions from students are welcome. The handwritten script will appear on the webpage of the lecture, where students can also find the relevant literature for selfstudy.
In tutorials we will discuss the solutions of homework assignments which would provide students with a practical knowledge of the material discussed in the lecture and will prepare them for doing research in condensed matter physics.
Literature
 P. Coleman, Introduction to ManyBody Physics
 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 ManyBody Systems
Module Exam
Description of exams and course work
There will be a written exam of 90 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using calculation problems and comprehension questions.
For example an assignment in the exam might be:
 Using perturbation theory, calculate the Landau parameters for fermions with a weak shortrange potential
 What is the main difference between Luttinger and Fermi liquids
 Analyze the fermionic energy spectrum and derive the Chern number of a chiral superconductor
 What are anyons and why they emerge only in twodimensional world?
Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.
There will be a bonus (one intermediate stepping of "0,3" to the better grade) on passed module exams (4,3 is not upgraded to 4,0). The bonus is applicable to the exam period directly following the lecture period (not to the exam repetition) and subject to the condition that the student passes the midterm of active participation in the tutorials and at least 50% of exercise points
Exam Repetition
The exam may be repeated at the end of the semester.