Advanced Methods in Quantum ManyBody Theory
Module PH2297
Module version of SS 2021 (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  

SS 2021  SS 2020 
Basic Information
PH2297 is a semester module in English language at Master’s level which is offered in summer semester.
This Module is included in the following catalogues within the study programs in physics.
 Specific catalogue of special courses for condensed matter physics
 Complementary catalogue of special courses for nuclear, particle, and astrophysics
 Complementary catalogue of special courses for Biophysics
 Complementary catalogue of special courses for Applied and Engineering Physics
 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 PH2297 is Michael Knap.
Content, Learning Outcome and Preconditions
Content
• Introduction to semiclassical methods, focusing on manybody dynamics. Beyond meanfield dynamics: truncated Wigner approximation (TWA).
• TWA in classical phase space: heuristic arguments, and derivation from nonequilibrium Keldysh path integral. Example: dynamics of the sineGordon model.
• TWA for outofequilibrium spin systems. Construction of discrete phase space, and discrete TWA.
• Introduction to exactly solvable models in classical and quantum statistical mechanics.
• Algebraic Bethe Ansatz.
• Introduction to the thermodynamics and outofequilibrium properties of 1d quantum integrable models.
• Quantum quenches, lack of thermalization and relazation to the Generalized Gibbs Ensemble: the example of the 1d Bose gas.
• Emergent hydrodynamics in integrable models.
• Introduction to group theory, lattice gauge theory, and projective symmetry group (PSG) theory
• Projective construction of quantum spin liquids using PSG. Example: Kitaev honeycomb model with (1) fourMajorana exact solution (2) projective construction solution
• Beyond meanfield theory: Guztwiller projection.
• Gorkov equation and anomalous Green’s function
• Phenomenological theory of multicomponentsuperconductivity
• Topological aspects of superconductivity
Learning Outcome
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  Advanced Methods in Quantum ManyBody Theory 
Knap, M.
Assistants: Bastianello, A.Jin, H.Lovas, L.Roy, A.Sim, G. 
eLearning 

UE  2  Exercise to Advanced Methods in Quantum ManyBody Theory 
Bastianello, A.
Jin, H.
Lovas, L.
Roy, A.
Sim, G.
Responsible/Coordination: Knap, M. 
Learning and Teaching Methods
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 exercise classes by the students themselves under supervision in order to develop the skills to explain a physics problem logically.
Media
Blackboard lectures, written notes for download, exercise sheets, course homepage
Literature
Module Exam
Description of exams and course work
The achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using presentations independently prepared by the students. The exam of 25 minutes consists of the presentation and a subsequent discussion.
For example an assignment in the exam might be:
 Sketch the derivation of the (standard phase space) TWA from the Keldysh path integral.
 Describe the main steps of the discrete (or cluster) truncated Wigner approximation for a spin1/2 chain.
 Sketch the derivation of the diagonalization of the Hamiltonian of the XXZ chain using Algebraic Bethe Ansatz.
 Calculate the ground state from the Bethe equations.
 What are the modular S and T matrices?
 Describe the stringnet construction for the toric code.
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.