Pekker, D. and Wunsch, B. and Kitagawa, T. and Manousakis, E. and Sørensen, A. S. and Demler, E. (2012) Signatures of the superfluid to Mott insulator transition in equilibrium and in dynamical ramps. Physical Review B, 86 (14). Art. No. 144527. ISSN 1098-0121. http://resolver.caltech.edu/CaltechAUTHORS:20120625-081713746
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We investigate the equilibrium and dynamical properties of the Bose-Hubbard model and the related particle-hole symmetric spin-1 model in the vicinity of the superfluid to Mott insulator quantum phase transition. We employ the following methods: exact-diagonalization, mean-field (Gutzwiller), cluster mean-field, and mean-field plus Gaussian fluctuations. In the first part of the paper we benchmark the four methods by analyzing the equilibrium problem and give numerical estimates for observables such as the density of double occupancies and their correlation function. In the second part, we study parametric ramps from the superfluid to the Mott insulator and map out the crossover from the regime of fast ramps, which is dominated by local physics, to the regime of slow ramps with a characteristic universal power law scaling, which is dominated by long wavelength excitations. We calculate values of several relevant physical observables, characteristic time scales, and an optimal protocol needed for observing universal scaling.
|Additional Information:||© 2012 American Physical Society. Received 12 June 2012; published 22 October 2012. It is our pleasure to thank M. Greiner, W. S. Bakr, and J. Simon for explaining their experimental setup and A. Polkovnikov for his encouragement and valuable insights. We would also like to thank G. Refael for valuable discussions, and the Aspen Center for Physics for its hospitality. This work was supported by a grant from the Army Research Office with funding from the DARPA OLE program, Harvard-MIT CUA, NSF Grant No. DMR-07-05472, AFOSR Quantum Simulation MURI, AFOSR MURI on Ultracold Molecules, the ARO-MURI on Atomtronics, the Lee A. DuBridge fellowship (D.P.), DFG Grant No 609/1-1 (B.W.), and The Danish National Research Foundation. The computations in this paper were run on the Odyssey cluster supported by the FAS Science Division Research Computing Group at Harvard University.|
|Group:||IQIM, Institute for Quantum Information and Matter|
|Classification Code:||PACS number(s): 64.60.Ht, 67.85.De, 67.85.Bc|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||19 Jul 2012 23:33|
|Last Modified:||09 Jan 2016 01:50|
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