Chin. Phys. Lett.  2012, Vol. 29 Issue (8): 083701    DOI: 10.1088/0256-307X/29/8/083701
ATOMIC AND MOLECULAR PHYSICS |
Self-Consistent Approach for Mapping Interacting Systems in Continuous Space to Lattice Models
WU Biao1**, XU Yong2, DONG Lin3, SHI Jun-Ren1
1International Center for Quantum Materials, Peking University, Beijing 100871
2Institute of Physics, Chinese Academy of Sciences, Beijing 100190
3Department of Physics and Astronomy, and Rice Quantum Institute, Rice University, Houston, Texas 77251-1892, USA
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Abstract We propose a general variational principle for mapping the interacting systems in continuous space to lattice models. Based on the principle, we derive a set of self-consistent nonlinear equations for the Wannier functions (or, equivalently for the Bloch functions). These equations show that the Wannier functions can be strongly influenced by the interaction and be significantly different from their non-interacting counterparts. The approach is demonstrated with interacting bosons in an optical lattice, and illustrated quantitatively by a simple model of interacting bosons in a double well potential. It is shown that the so-determined lattice model parameters can be significantly different from their non-interacting values.
Received: 23 February 2012      Published: 31 July 2012
PACS:  37.10.Jk (Atoms in optical lattices)  
  71.10.Fd (Lattice fermion models (Hubbard model, etc.))  
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https://cpl.iphy.ac.cn/10.1088/0256-307X/29/8/083701       OR      https://cpl.iphy.ac.cn/Y2012/V29/I8/083701
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