LEARNING OUTCOMES
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: 26.02.2024 - 31.05.2024
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
CONTENT, ASSESSMENT AND WORKLOAD
Content
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 materialsapplies in this implementation
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 and effective models
Lecture 4: Topological band structure theory
Lecture 5: Electrons in a magnetic field, quantum Hall effect and Landau Levels
Lecture 6: Superconductivity, Nambu representation and Majorana physics
Lecture 7: Magnetism, magnons, quantum magnetism and spinons
Lecture 8: Excitations and defects in quantum materials
Lecture 9: Tensor network and neural network many-body wavefunctions
Lecture 10: Machine learning for quantum materials
Lecture 11: Summary
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.
Workload
valid for whole curriculum period:
Contact teaching includes lectures and group presentations, group work and independent work.
DETAILS
Study Material
valid for whole curriculum period:
Many-Body Quantum Theory in Condensed Matter Physics, Henrik Bruus and Karsten Flensberg
The Oxford Solid State Basics, Steven H. Simon
Topological Quantum: Lecture Notes, Steven H. Simon
Solid State Physics, Giuseppe Grosso and Giuseppe Pastori Parravicini
Lecture notes: Solid State Theory, Manfred Sigrist
Lecture Notes: Introduction to Condensed Matter Theory, Titus Neupert
Substitutes for Courses
valid for whole curriculum period:
Prerequisites
valid for whole curriculum period:
SDG: Sustainable Development Goals
3 Good Health and Well-being
4 Quality Education
7 Affordable and Clean Energy
8 Decent Work and Economic Growth
9 Industry, Innovation and Infrastructure
FURTHER INFORMATION
Further Information
valid for whole curriculum period:
Teaching Language : English
Teaching Period : 2022-2023 Spring IV - V
2023-2024 Spring IV - VEnrollment :
Registration for Courses: In the academic year 2021-2022, registration for courses will take place on Sisu (sisu.aalto.fi) instead of WebOodi. Registration via WebOodi.