# 2019/20 Taught Postgraduate Module Catalogue

## PHYS5017M Quantum Many-Body Physics

### 15 creditsClass Size: 45

**Module manager:** Zlatko Papic**Email:** z.papic@leeds.ac.uk

**Taught:** Semester 2 View Timetable

**Year running** 2019/20

### Pre-requisite qualifications

Level 3 Physics or equivalent.### Pre-requisites

PHYS3382 | Advanced Quantum Mechanics |

**This module is not approved as an Elective**

### Module summary

Quantum systems of many interacting particles give rise to exotic phenomena such as superfluids, superconductors or even the new types of “topological” phases of matter. These systems exemplify the paradigm “More is Different”: they have emergent properties (new types of order and quasiparticle excitations) which make them more complex than their constituent parts. This module gives a modern introduction to quantum many-body systems from a point of view of quantum information. It establishes a foundation for the theoretical description (entanglement, symmetry breaking and topological order) and numerical simulations (matrix product states) of quantum many-body systems. The module will take you to the cutting edge of research into quantum many-body systems, highlighting their fundamental role in condensed matter and high-energy physics, but also future applications in quantum computing.### Objectives

On completion of this module, students should be able to demonstrate a basic knowledge and understanding of common physical laws that govern the physics of quantum many-body systems. Identify relevant principles and apply them to solve specific problems using field theory, exact solutions and/or numerical simulations.**Learning outcomes**

By the end of the module, you should be able to:

--understand and apply the methods of second quantisation to systems of many fermions and bosons;

--write down and diagonalise simple tight-binding models (e.g., graphene, the Kitaev model, etc.);

--solve a quantum many-body problem using the mean-field theory and Bogoliubov transformation;

--explain the concept of spontaneous symmetry breaking and quantum phase transition;

--study the properties of quantum spin chains via Jordan-Wigner transformation and mapping to Majorana fermions;

--define the concept of classical and quantum information, correlation and entanglement;

--use basic techniques of matrix product states to simulate quantum-many-body systems;

--understand the concept of a phase of matter, symmetry-breaking order and topological order (example: the quantum Hall effect);

--explain the basic properties of topological phases of matter and their applications in quantum computing.

### Syllabus

“More is Different”; Harmonic oscillators and quantum fields, second quantisation (examples: graphene, the Kitaev model, the Hubbard model); Mean-field theory (example: the Bogoliubov theory of a Bose superfluid); Quantum spin chains; Spontaneous symmetry breaking and quantum phase transition; Quantum and classical information and correlation, quantum entanglement; Matrix product states; the quantum Hall effect; Topological phases of matter and quantum computation.

### Teaching methods

Delivery type | Number | Length hours | Student hours |

Lecture | 22 | 1.00 | 22.00 |

Seminar | 4 | 1.00 | 4.00 |

Private study hours | 124.00 | ||

Total Contact hours | 26.00 | ||

Total hours (100hr per 10 credits) | 150.00 |

### Private study

As part of independent learning, the students will be asked to complete regular coursework. The rest of the time is planned for reading, working through the lecture notes and preparing for the final exam.### Opportunities for Formative Feedback

The monitoring of student progress will be performed regularly via coursework### Methods of assessment

**Coursework**

Assessment type | Notes | % of formal assessment |

Problem Sheet | Problem Sheets | 30.00 |

Total percentage (Assessment Coursework) | 30.00 |

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

**Exams**

Exam type | Exam duration | % of formal assessment |

Open Book exam | 2 hr 30 mins | 70.00 |

Total percentage (Assessment Exams) | 70.00 |

Students resitting the module will resit the examination only. The marks from the coursework will only be carried forward if it is to the student's advantage.

### Reading list

The reading list is available from the Library websiteLast updated: 30/04/2018

## Browse Other Catalogues

- Undergraduate module catalogue
- Taught Postgraduate module catalogue
- Undergraduate programme catalogue
- Taught Postgraduate programme catalogue

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