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arXiv · 1604.05664

Spectral analysis of two-dimensional Bose-Hubbard models

David Fischer·Darius Hoffmann·Sandro Wimberger
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Abstract

One-dimensional Bose-Hubbard models are well known to obey a transition from regular to quantum-chaotic spectral statistics. We are extending this concept to relatively simple two-dimensional many-body models. Also in two dimensions a transition from regular to chaotic spectral statistics is found and discussed. In particular, we analyze the dependence of the spectral properties on the bond number of the two-dimensional lattices and the applied boundary conditions. For maximal connectivity, the systems behave most regularly in agreement with the applicability of mean-field approaches in the limit of many nearest-neighbor couplings at each site.

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David Fischer, Darius Hoffmann, Sandro Wimberger. 2016-04-19. Spectral analysis of two-dimensional Bose-Hubbard models. https://doi.org/10.1103/physreva.93.043620

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