## 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. Introduction to vortex-boson duality in 2+1 dimensions.

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 dielectric solid, superfluid, normal metal and superconductor.

## 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

Calculate the properties of a superconductor within the Landau-Ginzburg theory

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

## Mode of instruction

See Brightspace

## Assessment method

Homework assignments 30% and a final examination 70%.

## 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)

### Brightspace

Registration for Brightspace occurs via uSis. How to sign up for classes click here

## Contact

Lecturer: Prof. Dr. J. Zaanen

Teaching assistants: Y. Herasymenko, Y. Cheipesh