High-order perturbation theory for correlated Boson systems

• Applicant: Professor Dr. Martin Holthaus
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: from 2009 to 2013
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 123473015

• Final Report Year: 2013

Final Report Abstract

In the course of this project we have adapted quantum mechanical high-order perturbation theory to the study of strongly correlated lattice Bosons, focusing on the Mott insulator-tosuperfluid quantum phase transition shown by the Bose-Hubbard model. We have computed several types of correlation functions for one-, two-, and three-dimensional lattices with arbitrary integer filling, and have determined the phase diagram for cubic, triangular, and hexagonal lattices. In the second part of this project we have extended our theoretical framework such that we are now able to monitor the emergence of both the condensate and the superfluid density upon crossing the phase boundary, and to extract the corresponding critical exponents. While satisfactory accuracy is achieved already at this point, we anticipate further refinements of our approach. New questions have emerged concerning the resummation of divergent perturbation series, and the identification of the actually relevant process-chain diagramms; these questions are presently being tackled. Thus, this project also will have a lasting impact on future research of our group.

Publications

• Process-chain approach to the Bose-Hubbard model: Ground-state properties and phase diagram, Phys. Rev. B 79, 224515 (2009)
  N. Teichmann, D. Hinrichs, M. Holthaus, and A. Eckardt
  
• Scaling property of the critical hopping parameters for the Bose-Hubbard model, Eur. Phys. J. B 71, 219-223 (2009)
  N. Teichmann and D. Hinrichs
  
• Reference data for phase diagrams of triangular and hexagonal bosonic lattices EPL 91, 10004 (2010)
  N. Teichmann, D. Hinrichs, and M. Holthaus