Hamburg 2009 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 3: Quantengase: Dynamik in Gittern

Q 3.7: Talk

Monday, March 2, 2009, 12:15–12:30, VMP 6 HS-A

Statistics of Schmidt coefficients and the simulability of complex quantum systems — •Hannah Venzl¹, Andrew J. Daley^2,3, Florian Mintert¹, and Andreas Buchleitner¹ — ¹Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany — ²Institut für Theoretische Physik, Universität Innsbruck, Technikerstr. 25, 6020 Innsbruck, Austria — ³Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria

We show that the transition from regular to chaotic spectral statistics in interacting many-body quantum systems has an unambiguous signature in the distribution of Schmidt coefficients dynamically generated from generic initial states. The characteristic redistribution that is observed on the transition to chaotic dynamics confirms that chaotic many body systems can not be described efficiently by local bases [1] what implies that techniques like the time-dependent Density Matrix Renormalization Group algorithm [2] loose their efficiency. We investigate these mechanisms on the tilted Bose-Hubbard model. However, the emergence of universal spectral properties allows to translate our conclusions to generic many-body quantum systems.

[1] H. Venzl, A. J. Daley, F. Mintert, and A. Buchleitner, arXiv:0808.3911

[2] G. Vidal, Phys. Rev. Lett. 91, 147902 (2003)