Berlin 2014 – wissenschaftliches Programm
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SYQS: Symposium Characterization and control of complex quantum systems
SYQS 2: Characterization and control of complex quantum systems II
SYQS 2.5: Vortrag
Freitag, 21. März 2014, 15:15–15:30, Audimax
Dynamical Algebras and Many-body Physics — •Zoltán Zimborás1, Robert Zeier2, Zoltán Kádár3, Michael Keyl2, and Thomas Schulte-Herbrüggen2 — 1University of the Basque Country (UPV/EHU), Bilbao, Spain — 2Technische Universität München (TUM), Germany — 3University of Leeds (UL), UK
Dynamical algebras, i.e., Lie algebras generated by Hamiltonians, are basic tools both in Quantum Control and Quantum Simulation Theory. In this talk, we will argue that these algebras might also have relevance in Many-Body Physics. By studying Lie closures of translation-invariant Hamiltonians, we show that nearest-neighbor Hamiltonians do not generate all translation-invariant interactions. We discuss the relevance of this result in simulating many-body dynamics. Furthermore, we point out that our results [1] also provides a surprising Lie algebraic explanation of a previous finding of ours concerning the absence of gap in quasifree models with (twisted) reflection-symmetry breaking [2].
[1] Z. Zimborás, R. Zeier, M. Keyl, and T. Schulte-Herbrüggen, ``A Dynamic Systems Approach to Fermions and Their Relations to Spins", arXiv:1211.2226.
[2] Z. Kádár and Z. Zimborás, ``Entanglement entropy in quantum spin chains with broken reflection invariance", Phys. Rev. A 82, 032334 (2010).