Quantum field theory for the three-body constrained lattice Bose gas. I. formal developments

S. Diehl, M. Baranov, A. J. Daley, P. Zoller

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31 Citations (Scopus)


We develop a quantum field theoretical framework to analytically study the three-body constrained Bose-Hubbard model beyond mean field and noninteracting spin wave approximations. It is based on an exact mapping of the constrained model to a theory with two coupled bosonic degrees of freedom with polynomial interactions, which have a natural interpretation as single particles and two-particle states. The procedure can be seen as a proper quantization of the Gutzwiller mean field theory. The theory is conveniently evaluated in the framework of the quantum effective action, for which the usual symmetry principles are now supplemented with a "constraint principle" operative on short distances. We test the theory via investigation of scattering properties of few particles in the limit of vanishing density, and we address the complementary problem in the limit of maximum filling, where the low-lying excitations are holes and diholes on top of the constraint-induced insulator. This is the first of a sequence of two papers. The application of the formalism to the many-body problem, which can be realized with atoms in optical lattices with strong three-body loss, is performed in a related work.

Original languageEnglish
Article number064509
Number of pages19
JournalPhysical Review B: Condensed Matter and Materials Physics
Issue number6
Publication statusPublished - 1 Aug 2010
Externally publishedYes


  • lattice theory
  • bosons
  • spin models


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