### 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.

Original language | English |
---|---|

Article number | 064509 |

Number of pages | 19 |

Journal | Physical Review B: Condensed Matter and Materials Physics |

Volume | 82 |

Issue number | 6 |

DOIs | |

Publication status | Published - 1 Aug 2010 |

Externally published | Yes |

### Fingerprint

### Keywords

- lattice theory
- bosons
- spin models

### Cite this

*Physical Review B: Condensed Matter and Materials Physics*,

*82*(6), [064509]. https://doi.org/10.1103/PhysRevB.82.064509

}

*Physical Review B: Condensed Matter and Materials Physics*, vol. 82, no. 6, 064509. https://doi.org/10.1103/PhysRevB.82.064509

**Quantum field theory for the three-body constrained lattice Bose gas. I. formal developments.** / Diehl, S.; Baranov, M.; Daley, A. J.; Zoller, P.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Quantum field theory for the three-body constrained lattice Bose gas. I. formal developments

AU - Diehl, S.

AU - Baranov, M.

AU - Daley, A. J.

AU - Zoller, P.

PY - 2010/8/1

Y1 - 2010/8/1

N2 - 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.

AB - 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.

KW - lattice theory

KW - bosons

KW - spin models

UR - http://www.scopus.com/inward/record.url?scp=77957553859&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.82.064509

DO - 10.1103/PhysRevB.82.064509

M3 - Article

VL - 82

JO - Physical Review B: Condensed Matter and Materials Physics

JF - Physical Review B: Condensed Matter and Materials Physics

SN - 1098-0121

IS - 6

M1 - 064509

ER -