Entanglement and Quantum Phase Transitions

Seminar (MVSem)

Dozenten: Prof. Dr. Thomas Gasenzer and Prof. Dr. Markus Oberthaler

Mon, 14:15 - 15:45, Fri, 15:15 - 16:45 (special dates). Room: INF 227, SR 1.404 N (Mon); SB 1.107 (Fri). [LSF]
1. Session: Fr., 17.04. (Discussion and distribution of topics); Seminar starts on 08.06.

Interested? Please send me an E-mail.

Topics - Prerequisites - Literature - Additional Material

Objectives see Master course manual (MVSem).

Preliminary topics (Seminar Schedule)

  1. Introduction to quantum phase transitions
  2. Experiments on solid-state systems
  3. Quantum criticality in ultracold atomic gases
  4. Entanglement measures in many-body systems
  5. Bipartite Entanglement
  6. Entanglement entropy
  7. Localizable entanglement
  8. Thermal entanglement
  9. Multipartite entanglement
  10. Spin squeezing and entanglement
  11. Dynamics of entanglement near criticality

Prerequisites (necessary and useful knowledge):
  • Bachelor courses (mandatory); Useful are special courses in either of the fields Theoretical Statistical Physics, Quantum Field Theory, Condensed Matter Physics, Advanced Atomic, Molecular and Optical Physics.

    See also this semester's lecture by T. Gasenzer on Quantum Phase Transitions.

Literature

Literature specific to the topics: see Seminar Schedule.

General literature (in alphabetic order):

Textbooks on quantum field theory
  • Michael E. Peskin, Daniel V. Schroeder An introduction to quantum field theory. Westview, Boulder, 2006. [ Google books | HEIDI ]
  • Xiao-Gang Wen, Quantum Field Theory of Many-Body Systems. OUP, Oxford, 2010. [ Google books | HEIDI ]
Critical phenomena and quantum phase transitions
  • D. Belitz und T.R. Kirkpatrick, in J. Karkheck (Hrsg.), Dynamics: Models and kinetic methods for non-equilibrium many-body systems. Kluwer, Dordrecht (2000). [ Google books | HEIDI ]
  • John Cardy, Scaling and renormalization in statistical physics. CUP, Cambridge, 2003. [ Google books | HEIDI ]
  • Lincoln D. Carr (Ed.), Understanding quantum phase transitions. CRC-Press, Boca Raton, 2011. [ Google books | HEIDI ]
  • Nigel Goldenfeld, Lectures on phase transitions and the renormalization group. Addison-Wesley, Reading, 1992. [ Google books | HEIDI ]
  • Igor Herbut, A modern approach to critical phenomena. CUP, Cambridge, 2007. [ Google books | HEIDI ]
  • Subir Sachdev, Quantum Phase Transitions. CUP, Cambridge, 2011. [ Google books | HEIDI (incl. online) ]
  • S. L. Sondhi, S. M. Girvin, J. P. Carini, and D. Shahar, Continuous quantum phase transitions. Rev. Mod. Phys. 69, 315 (1997). [ arXiv:cond-mat/9609279 ]
  • Jean Zinn-Justin, Quantum field theory and critical phenomena. Clarendon, Oxford, 2004. [ Google books | HEIDI ]
Entanglement Quantum phase transitions and entanglement
  • Luigi Amico, Rosario Fazio, Andreas Osterloh, and Vlatko Vedral, Entanglement in many-body systems. Rev. Mod. Phys. 80, 517 (2008). [ arXiv:quant-ph/0703044v3 ]
  • Eduardo Fradkin, Field theories of condensed matter physics. (Chap. 17) CUP, Cambridge, 2013. [ Google books | HEIDI ]
  • Maciej Lewenstein, Anna Sanpera and Veronica Ahufinger, Ultracold atoms in optical lattices. Simulating quantum many-body systems. (Chap. 12.3) OUP, Oxford, 2012. [ Google books | HEIDI ]

Additional Material