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

S. Diehl, M. Baranov, A. J. Daley, and P. Zoller
Phys. Rev. B 82, 064509 – Published 13 August 2010

Abstract

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 [S. Diehl, M. Baranov, A. Daley, and P. Zoller, Phys. Rev. B 82, 064510 (2010)].

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  • Received 29 March 2010

DOI:https://doi.org/10.1103/PhysRevB.82.064509

©2010 American Physical Society

Authors & Affiliations

S. Diehl1,2, M. Baranov1,2,3, A. J. Daley1,2, and P. Zoller1,2

  • 1Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, A-6020 Innsbruck, Austria
  • 2Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
  • 3RRC “Kurchatov Institute,” Kurchatov Square 1, 123182 Moscow, Russia

See Also

Quantum field theory for the three-body constrained lattice Bose gas. II. Application to the many-body problem

S. Diehl, M. Baranov, A. J. Daley, and P. Zoller
Phys. Rev. B 82, 064510 (2010)

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Vol. 82, Iss. 6 — 1 August 2010

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