## Admission Requirements

Bachelor of Physics including an introduction to solid state physics , understanding electron band structure, phonons, etcetera.

Master courses: Quantum Theory, Statistical Physics a. Recommended, although not mandatory: Statistical Physics b and effective field theory.

## Description

The course gives an introduction into the theory describing the emergence of macroscopic matter from interacting microscopic constituents.

This revolves around the explanation of emergence principles such as spontaneous symmetry breaking and long range order, adiabatic continuity, collective excitations such as Goldstone bosons, quasiparticles, and topological excitations, as they arise both in weakly- and strongly interacting systems.

We will explain the mathematical theories underlying the understanding of the following states of matter:

The crystal, including the theory of quantum elasticity describing phonons and phonon interactions.

Magnetism, with a focus on Mott-insulators and superexchange; spin-wave theory.

Spin- and charge density waves in the weak coupling limit: the concept of nesting.

The microscopic theory of superconductivity and superfluidity: from local pairs to the Bardeen-Cooper-Schrieffer theory.

The Ginzburg-Landau effective field theory of macroscopic superconductivity.

The Fermi-liquid including the origin of quasi-electrons, zero sound and plasmons.

With the help of the second quantization approach, perturbation theory and the mean-field theory the course introduces a number of fundamental concepts such as long-range order, spontaneous symmetry breaking, elementary, collective and topological excitations. These general concepts are illustrated on a range of archetypal examples such as crystalline solids, magnets, superfluids and superconductors and Fermi-liquid metals.

## Course objectives

The course will provide students with an exercise ground to apply the mathematical techniques of quantum many body theory. This includes the second quantization formalism, Green's functions/propagators, linear response theory, perturbation theory, mean field theory, quantum statistical physics and elementary applications of the path-integral formalism.

At the end of the course you will be able to

Construct second-quantized models of quantum many-body systems

Calculate thermodynamic properties of model systems

Calculate linear response functions (e.g. magnetic susceptibility) of model systems

Describe elementary excitations of a model system

Use perturbation theory in a many-body system

Apply mean-field theory to interacting systems of bosons and fermions

Construct topological excitations of a quantum fluid

Use the random phase approximation

Derive and solve the BSC equation for the superconducting gap

Compute the pole strenght and effective mass of Fermi-liquid quasiparticles.

### Transferable skills

An intellectual skill that is specific for condensed matter physics is associated with the important role of toy models, which are not literal, let alone quantitative, having however the capacity of capturing the essence of emergence phenomena. In addiiton, it is the historic arena where "strong emergence" physics came on the foreground: "the whole is so different from the sum of the parts that the latter are no longer discernable." In the course of time this has taken over all of fundamental physics, e.g. the standard of model of high energy physics is "Ginzburg-Landau with non-Abelian bells and whistles." To learn to handle this is the last reprogramming of the brane required to appreciate the present frontier of physics.

## Timetable

Physics Schedule

For detailed information go to Timetable in Brightspace

In MyTimetable, you can find all course and programme schedules, allowing you to create your personal timetable. Activities for which you have enrolled via MyStudyMap will automatically appear in your timetable.

Additionally, you can easily link MyTimetable to a calendar app on your phone, and schedule changes will be automatically updated in your calendar. You can also choose to receive email notifications about schedule changes. You can enable notifications in Settings after logging in.

Questions? Watch the video, read the instructions, or contact the ISSC helpdesk.

**Note:** Joint Degree students from Leiden/Delft need to combine information from both the Leiden and Delft MyTimetables to see a complete schedule. This video explains how to do it.

## Mode of instruction

See Brightspace

## Assessment method

Homework assignments 40% and a final examination 60%.

## Reading list

A set of lecture notes prepared by the lecturer.

Background reading (not mandatory):

P.Phillips, "Advanced solid state physics" (Cambridge Univ. Press, 2012).

A. Altland and B. Simons, "Condensed matter field theory" (Cambridge Univ. Press, 2010)

P. Coleman, "Introduction to many body physics" (Cambridge Univ. Press, 2016)

P. Nozieres and D. Pines, "Theory of Quantum Liquids"(Avalon publishing, 1999)

## Registration

As a student, you are responsible for enrolling on time through MyStudyMap.

In this short video, you can see step-by-step how to enrol for courses in MyStudyMap.

Extensive information about the operation of MyStudyMap can be found here.

There are two enrolment periods per year:

Enrolment for the fall opens in July

Enrolment for the spring opens in December

See this page for more information about deadlines and enrolling for courses and exams.

**Note:**

It is mandatory to enrol for all activities of a course that you are going to follow.

Your enrolment is only complete when you submit your course planning in the ‘Ready for enrolment’ tab by clicking ‘Send’.

Not being enrolled for an exam/resit means that you are not allowed to participate in the exam/resit.

## Contact

Lecturer: Prof. Dr. J. Zaanen

## Remarks

**Software**

Starting from the 2024/2025 academic year, the Faculty of Science will use the software distribution platform Academic Software. Through this platform, you can access the software needed for specific courses in your studies. For some software, your laptop must meet certain system requirements, which will be specified with the software. It is important to install the software before the start of the course. More information about the laptop requirements can be found on the student website.