# Quantum Many-Body Physics

## Module PH2256

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.

### Module version of WS 2022/3 (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 2022/3 | WS 2021/2 | 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 Elite-Master Program Theoretical and Mathematical Physics (TMP)

If not stated otherwise for export to a non-physics 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 Michael Knap.

### Content, Learning Outcome and Preconditions

#### Content

This module provides an introduction into quantum many-body physics. We will cover basic quantum field-theoretical methods and their application to various many-body 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 many-body problem:

emergence and collective behavior, quantum fields, second quantization - Path integral formulation of quantum field theory
**:**

single-particle quantum mechanics from the

- Linear response theory

response functions, fluctuation-dissipation theorem, conductivity of Fermi gas - Fermi liquid theory:

Fermi liquid ground state, quasiparticles and their stability, collective modes, Landau damping, non-Fermi liquids - Luttinger liquids:

pecularities of physics in one dimension, Luttinger model, basic of bosonization, correlation functions, relation to conformal field theories and two-dimensional classical XY model - Superfluids and superconductors:

physical properties of superfluids and superconductors, BCS theory, phase stiffness, vortices, rotating superfluids, boson-vortex duality in two dimensions, Berezinskii-Kosterlitz-Thouless transition, chiral superfluids and superconductors - Quantum Hall fluids:

basics of quantum Hall effect, flux attachment and Chern-Simons theory, topological order and anyons in fractional quantum Hall fluids, abelian Chern-Simons theory and the hierarchy of quanum Hall states, edge of quantum Hall fluids, non-abelian 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 many-body problems
- understand theoretical paradigms that are central in modern condensed matter physics
- have a working knowledge of the physics of Fermi liquids, one-dimensional 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 Many-Body Physics | Knap, M. |
singular or moved dates |
eLearning |

UE | 2 | Exercise to Quantum Many-Body Physics |
Arzi, O.
Birnkammer, S.
Zechmann, P.
Zerba, C.
Responsible/Coordination: Knap, M. |
dates in groups | |

UE | 2 | Open Tutorial to Quantum Many-Body Physics |
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 web-page of the lecture, where students can also find the relevant literature for self-study.

In tutorials we will discuss the solutions of home-work 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 Many-Body 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 Many-Body Systems

### Module Exam

#### Description of exams and course work

The examination for the module is taken in the form of an examination course.

The exam course consists of a written exam (90 minutes) and an essay. In the run-up to the exam, each student is given a topic on which an essay is written. This essay is handed in with the written exam and represents one third of the total score. In the essay, the students show by means of an example that they are able to understand current scientific work in the field of quantum many-particle physics and to comprehend the derivations contained therein with the help of the methods taught in the course.

The subsequent written exam of 90 minutes covers all topics of the module. In this examination, the achievement of the competences described in the section Learning Outcomes is tested at least at the level of knowledge indicated there by means of knowledge and comprehension questions. Examination task could be for example:

- Calculate perturbatively the Landau parameters for fermions with a weak short-range potential.
- What are the main differences between Luttinger and Fermi fluids?
- Analyze the fermionic energy spectrum and derive the Chern number of a chiral superconductor.
- What are anyons, and why do they appear only in the two-dimensional world?

The grade will be based on 2/3 of the exam and 1/3 of the essay.

Translated with www.DeepL.com/Translator (free version)

#### Exam Repetition

The exam may be repeated at the end of the semester.

#### Current exam dates

Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.

Title | |||
---|---|---|---|

Time | Location | Info | Registration |

Exam to Quantum Many-Body Physics | |||

Fri, 2023-02-17, 11:30 till 13:00 | 1550 1550 |
till 2023-01-15 (cancelation of registration till 2023-02-10) | |

Thu, 2023-03-30, 11:00 till 12:30 | 1550 1550 |
till 2023-03-20 (cancelation of registration till 2023-03-23) |