Theoretical Physics

23 October 2013
Time: 15:00 to 16:00
Location: SR 8.62 in EC Stoner

Zoltan Zimboras (Bilbao, Spain)

Dynamical Algebras and Many-body Physics

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





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