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Quanteninformationsmethoden in der Vielteilchenphysik
Quantum Information Methods in Many-Body Physics

Modul PH2269

Diese Modulbeschreibung enthält neben den eigentlichen Beschreibungen der Inhalte, Lernergebnisse, Lehr- und Lernmethoden und Prüfungsformen auch Verweise auf die aktuellen Lehrveranstaltungen und Termine für die Modulprüfung in den jeweiligen Abschnitten.

Basisdaten

PH2269 ist ein Semestermodul in Englisch auf Master-Niveau das im Sommersemester angeboten wird.

Das Modul ist Bestandteil der folgenden Kataloge in den Studienangeboten der Physik.

  • Allgemeiner Spezialfachkatalog Physik
  • Spezifischer Spezialfachkatalog Physik der kondensierten Materie
  • Spezialisierung im Elitemasterstudiengang Theoretische und Mathematische Physik (TMP)

Soweit nicht beim Export in einen fachfremden Studiengang ein anderer studentischer Arbeitsaufwand ("Workload") festgelegt wurde, ist der Umfang der folgenden Tabelle zu entnehmen.

GesamtaufwandPräsenzveranstaltungenUmfang (ECTS)
150 h 45 h 5 CP

Inhaltlich verantwortlich für das Modul PH2269 ist Ignacio Cirac.

Inhalte, Lernergebnisse und Voraussetzungen

Inhalt

Quantum many-body systems exhibit a rich variety of interesting physical phenomena, such as systems with exotic "topological" order which cannot be captured by Landau's theory of phases, and in which the system organizes globally in its quantum correlations rather than locally. The heart of such phenomena is formed by quantum correlations, this is, entanglement, which is at the heart of quantum information theory. This has given rise to a new research area at the intersection of quantum information theory and quantum many-body physics, where methods from quantum information are applied to the structure of these systems. This lecture will give a comprehensive introduction to this new research field. A special focus will be formed by the field of Tensor Network States, which provide an entanglement based description of quantum many-body states.

Topics covered include:

  • Quantum many body systems
  • Entanglement and the area law
  • Matrix Product States (MPS)
  • Variational simulations based on MPS, the DMRG method
  • Simulation of thermal states and time evolution
  • Projected Entangled Pair States (PEPS)
  • topological order
  • fermionic systems

Lernergebnisse

After successful completion of the module the students are able to

  1. understand the entanglement properties of many-body systems.
  2. identify the properties relevant for a state with low entanglement.
  3. give the construction of a matrix product state.
  4. design a variational algorithm based on matrix product states.
  5. derive the classification of symmetry protected phases in one dimension.
  6. understand the way in which symmetries are realized in matrix product states.
  7. provide examples for matrix product states, such as the AKLT state.
  8. start a research project in the field of tensor network states.

Voraussetzungen

Quantum mechanics, in particular also many-body quantum mechanics and second quantisation. Knowledge in quantum information and/or condensed matter physics is helpful, but not required.

Lehrveranstaltungen, Lern- und Lehrmethoden und Literaturhinweise

Lehrveranstaltungen und Termine

ArtSWSTitelDozent(en)Termine
VO 2 Quantum Information Methods in Many-Body Physics Cirac, I. Schuch, N. Fr, 14:00–17:00
Fr, 14:15–16:15
sowie einzelne oder verschobene Termine
UE 1 Übung zu Quanteninformationsmethoden in der Vielteilchenphysik Schuch, N.

Lern- und Lehrmethoden

In the lecture, the learning content will be presented in a form structured according to the different subtopics such basic structure, analytical theory, and numerical realization.  The cross-references between the different topics and the underlying universal principle of entanglement and the area law will be made clear at each level.  Students will be engaged in scientific discussions about the topic and will be encouraged to build their analytical skills as well as their numerical abilities.

In the exercise, the content of the lecture will be deepened by working out specific problems and examples as well as hands-on programming tutorials, amond other measures.  The students will thus be enabled to carry out research talks in the field on their own.

Medienformen

Blackboard, presentations (slides), electronic board (with handouts).  Exercises will be done in small groups with individual supervision.

Literatur

https://arxiv.org/abs/1306.2164

https://arxiv.org/abs/1008.3477

Modulprüfung

Beschreibung der Prüfungs- und Studienleistungen

There will be an oral exam of about 25 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and sample calculations.

For example an assignment in the exam might be:

  • What is the area law?
  • What is a Matrix Product State?
  • What is the basic idea of the DMRG algorithm?
  • How can we use Matrix Product States to simulate time evolution?

Participation in the tutorials is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.

Wiederholbarkeit

Eine Wiederholungsmöglichkeit wird am Semesterende angeboten.

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