Please note! Course description is confirmed for two academic years, which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.


The aim of this course is to provide students with the fundamental concepts of modern solid-state theory, focusing on emergent phenomena in quantum materials. The course connects with a variety of concepts from previous courses of statistical physics, quantum mechanics and electromagnetism. The course especially emphasizes the importance of collective behavior, quasiparticles and emergent behavior in complex quantum systems.  Among others, the course presents the topological characterization of electronic systems, spontaneous symmetry and emergent quasiparticles, superconductivity, quantum spin liquids, fractional quantum Hall effect, tensor network and neural network quantum many-body algorithms and machine learning applied to quantum materials.

Credits: 5

Schedule: 27.02.2023 - 07.06.2023

Teacher in charge (valid for whole curriculum period):

Teacher in charge (applies in this implementation): Jose Lado Villanueva

Contact information for the course (applies in this implementation):

CEFR level (valid for whole curriculum period):

Language of instruction and studies (applies in this implementation):

Teaching language: English. Languages of study attainment: English


  • valid for whole curriculum period:

    Selected topics on quantum materials and quantum matter: topological insulators, fractional quantum Hall effect, superconductors and Majorana physics, quantum spin-liquids, symmetry broken states, tensor-networks and quantum machine learning.

    List of lectures:
    Lecture 1: Second quantization, mean-field and spontaneous symmetry breaking
    Lecture 2: Symmetries, reciprocal space, Bloch’s theorem
    Lecture 3: Band structure theory, tight binding, nearly free electron and k.p
    Lecture 4: Linear response theory, Kubo formalism
    Lecture 5: Topological band structure theory
    Lecture 6: Electrons in a magnetic field, quantum Hall effect and Landau Levels
    Lecture 7: Fractionalization in quantum materials: The fractional quantum Hall effect
    Lecture 8: Superconductivity, Nambu representation and Majorana physics
    Lecture 9: Magnetism, magnons, quantum magnetism and spinons
    Lecture 10: Numerical methods: density functional theory and tensor network formalism
    Lecture 11: Machine learning in quantum materials

Assessment Methods and Criteria
  • valid for whole curriculum period:

    Lectures with pre-assignments, group presentations on selected topics in quantum materials, individual exercise and oral exam. Grading is based on weighted average of the previous tasks.

  • valid for whole curriculum period:

    Contact teaching includes lectures and group presentations, group work and independent work.


Substitutes for Courses


Further Information
  • valid for whole curriculum period:

    Teaching Language : English

    Teaching Period : 2022-2023 Spring IV - V
    2023-2024 Spring IV - V

    Enrollment :

    Registration for Courses: In the academic year 2021-2022, registration for courses will take place on Sisu ( instead of WebOodi. Registration via WebOodi.