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

Journal Article · Sun Aug 01 00:00:00 EDT 2010 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/PHYSREVB.82.064509· OSTI ID:21436002

Diehl, S; Daley, A J; Zoller, P ^[1]; Baranov, M ^[1]

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1. Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, A-6020 Innsbruck (Austria)

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)].

• OSTI ID: 21436002
• Journal Information: Physical Review. B, Condensed Matter and Materials Physics, Vol. 82, Issue 6; Other Information: DOI: 10.1103/PhysRevB.82.064509; (c) 2010 The American Physical Society; ISSN 1098-0121
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
APPROXIMATIONS
ATOMS
BOSE-EINSTEIN GAS
DEGREES OF FREEDOM
DENSITY
EXCITATION
HUBBARD MODEL
INTERACTIONS
LOSSES
MEAN-FIELD THEORY
POLYNOMIALS
QUANTIZATION
QUANTUM FIELD THEORY
SCATTERING
SPIN WAVES
SYMMETRY
THREE-BODY PROBLEM
CALCULATION METHODS
CRYSTAL MODELS
ENERGY-LEVEL TRANSITIONS
FIELD THEORIES
FUNCTIONS
MANY-BODY PROBLEM
MATHEMATICAL MODELS
PHYSICAL PROPERTIES