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Lehrende/r: Jun.-Prof. Dr. Roman Orùs; Jun.-Prof. Dr. Matteo Rizzi
Veranstaltungsart:
Vorlesung/Übung
Anzeige im Stundenplan:
Entanglement in many
Semesterwochenstunden:
4
Credits:
6,0
Unterrichtssprache:
Englisch
Min. | Max. Teilnehmerzahl:
- | -
Voraussetzungen / Organisatorisches:
Prerequisite for this course is a fair knowledge of the following topics:
- quantum mechanics (Hilbert spaces, probabilities, unitary evolutions, spin and Pauli matrices, composite systems, possibly density matrices)
- basic quantum many-body theory and statistical mechanics concepts (Fermionic/Bosonic statistics, 2nd quantization formalism, possibly some concept of renormalization and/or critical exponents)
- basic computer programming (language is not too important: e.g. Fortran, C++, Matlab, Mathematica)
The class will include a practical part consisting in writing up a simple Density Matrix Renormalization Group (henceforth, DMRG) code in order to solve some simple problems and to provide you a potential instrument for further studies in many fields.
Inhalt:
After an introduction of entanglement and other quantum information concepts (overlapping to other classes), we will focus on their use as tools to investigate many-body systems and their quantum phases, both from the conceptual and from the computational point of view. The concepts and tools are so general that they can find application in different current research fields like, e.g., cold atoms in optical lattices, spins in magnetic materials, electrons in solids, quantum chemistry, topological materials, and so on.
The theoretical aspect will be complemented by a practical part, via the development of your own simple Density Matrix Renormalization Group (henceforth, DMRG) code in order to solve some simple problems (e.g. compute low energy spectra and/or structure factors of toy systems) and possibly open the path for extended master thesis works.
Empfohlene Literatur:
We refer here to a couple of books but mainly to good reviews and lecture notes.
1) do not feel scared by the articles, they are just as good as (or even more than) book chapters (and anyway we can help you through)
2) in case you are not able to download them (it should be possible from the Biblio-Accounts), let us know and we will provide PDF's to you.
- Quantum Computation and Quantum Information - Nielsen and Chuang - Cambridge Univ. Press
- Lecture Notes on Quantum Information - Preskill - www.theory.caltech.edu/people/preskill/ph229
- Computational Many-Particle Physics - edited by H Fehske, R Schneider, and A Weiße - Springer 2008 - http://link.springer.com/book/10.1007/978-3-540-74686-7/page/1
- selected chapters from Ultracold atoms in optical lattices - Lewenstein, Sanpera and Ahufinger - Oxford Univ. Press
- special issue of Journal of Physics A, Vol 42, Num 50 - edited by Calabrese, Cardy, Doyon
- Amico, Fazio, Osterloh, Vedral - Rev. Mod. Phys. 80, 517 (2008) - arXiv:quant-ph/0703044
- Horodecki^4 - Rev. Mod. Phys. 81, 865 (2009) - arXiv:quant-ph/0702225
- Eisert, Cramer, Plenio - Rev. Mod. Phys. 82, 277 (2010) - arXiv:0808.3773
- Schollwöck - Rev. Mod. Phys. 77, 259 (2005) - arXiv:cond-mat/0409292
- Schollwöck - Ann. Phys. 326, 96 (2011) - arXiv:1008.3477
- Cirac - lecture notes from Les Houches - arXiv:1205.3742
- Verstraete, Cirac, Murg - Adv. Phys. 57, 143 (2008) - arXiv:0907.2796
- Cirac, Verstraete - Jour. Phys. A 42, 504004 (2009) - arXiv:0910.1130
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