Hamburg 2009 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 7: Quantengase: Bosonen im Gitter I
Q 7.5: Talk
Monday, March 2, 2009, 15:00–15:15, VMP 6 HS-A
Ginzburg-Landau Theory for Quantum Phase Transitions in Bosonic Lattices — Barry Bradlyn1, •Francisco Ednilson Alves dos Santos2, and Axel Pelster2,3 — 1Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA — 2Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany — 3Fachbereich Physik, Universität Duisburg-Essen, Lotharstrasse 1, 47048 Duisburg, Germany
We work out a Ginzburg-Landau theory for investigating quantum phase transitions in lattice Bose systems at arbitrary temperature [1]. To this end we expand the grand-canonical free energy as a double power series in both the tunneling and a symmetry breaking source term. Then an order parameter field is introduced, and the underlying effective action is derived via a Legendre transformation. Determining the Ginzburg-Landau expansion to first order in the tunneling term, expressions for the Mott insulator–superfluid phase boundary, condensate density, average particle number, and compressibility are derived. Additionally, excitation spectra in the ordered phase are found by considering both longitudinal and transverse variations of the order parameter. Although our effective action approach yields the same Mott insulator - superfluid phase boundary to first order in the tunneling than standard mean-field theory, our predictions turn out to be superior to the mean-field results deeper into the superfluid phase.
[1] B. Bradlyn, F.E.A. dos Santos, and A. Pelster, Phys. Rev. A (in press), eprint: arXiv:0809.0706.