Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1404.0704 · Physica Scripta

Mean-field approaches to the Bose–Hubbard model with three-body local interaction

Tomasz Sowiński, Ravindra W. Chhajlany

Published Apr 1, 2014• 11 citations
arXivHTMLPDF

Abstract

The zero temperature properties of the generalized Bose–Hubbard model including three-body interactions are studied on a mean-field level. We obtain analytical results using the so-called perturbative mean-field method and more detailed numerical results using the Gutzwiller product state variational ansatz. These two approaches yield equivalent results which compare well on a qualitative level with recent exact results obtained in the literature.

DOI
10.1088/0031-8949/2014/t160/014038

Related papers

Equivalence of Gutzwiller and slave-boson mean-field theories for multiband Hubbard models

Jörg Bünemann, Florian Gebhard

We demonstrate that a recently introduced slave-boson mean-field theory is equivalent to our Gutzwiller theory for multiband Hubbard models with general onsite interactions. We relate the different objects that appear in both approaches at zero temperature and discuss the limitations of both methods.

arXiv:0709.1413•Physical Review B•Nov 20, 2007•73 citations

Extended Bose—Hubbard model with pair hopping on triangular lattice

Yan-Cheng Wang, Wan-Zhou Zhang, Hui Shao +1 more

We study systematically an extended Bose—Hubbard model on the triangular lattice by means of a meanfield method based on the Gutzwiller ansatz. Pair hopping terms are explicitly included and a three-body constraint is applied. The zero-temperature phase diagram and a variety of quantum phase transitions are investigated in great detail. In particular, we show the existence and the stability of the pair supersolid phase.

arXiv:1302.1376•Chinese Physics B•Sep 1, 2013•11 citations

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

Sebastian Diehl, M. Baranov, Andrew J. Daley +1 more

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)].

arXiv:0912.3192•Physical Review B•Aug 13, 2010•31 citations

Mean-field phase diagram of the extended Bose-Hubbard model of many-body cavity quantum electrodynamics

Lukas Himbert, Cecilia Cormick, Rebecca Kraus +2 more

We investigate the mean-field phase diagram of the Bose-Hubbard model with infinite-range interactions in two dimensions. This model describes ultracold bosonic atoms confined by a two-dimensional optical lattice and dispersively coupled to a cavity mode with the same wavelength as the lattice. We determine the ground-state phase diagram for a grand-canonical ensemble by means of analytical and numerical methods. Our results mostly agree with the ones reported in Dogra et al. [N. Dogra, F. Brennecke, S. D. Huber, and T. Donner, Phys. Rev. A 94, 023632 (2016)], and have a remarkable qualitative agreement with the quantum Monte Carlo phase diagrams of Flottat et al. [T. Flottat, L. de Forges de Parny, F. H\'ebert, V. G. Rousseau, and G. G. Batrouni, Phys. Rev. B 95, 144501 (2017)]. The salient differences concern the stability of the supersolid phases, which we discuss in detail. Finally, we discuss differences and analogies between the ground-state properties of all-connected bosons with the ones predicted for repulsively interacting dipolar bosons in two dimensions.

arXiv:1902.05801•Physical Review A•Apr 30, 2019•24 citations

Bose–Hubbard models: methods of treatment

Maciej Lewenstein, Anna Sanpera, V. Ahufinger

This chapter reviews various theoretical methods that can be applied to investigate Bose–Hubbard models. In particular, it discusses the Bogolyubov method, strong coupling expansion, the perturbative mean field approach and the Gutzwiller method, exact diagonalization, quantum Monte Carlo methods, semi-classical phase space methods, and methods specifics for 1D (Wigner-Jordan transformation, Bethe ansatz, bosonization). The chapter end with a discussion about numerical renormalization approaches in 1D (DMRG, MPS) and 2D (PEPS; MERA).

Oxford University Press eBooks•Mar 8, 2012•1 citation

A phase-space method for the Bose–Hubbard model: application to mean-field models

P Jain, Crispin W. Gardiner

We present a phase-space method for the Bose–Hubbard model based on the Q-function representation. In particular, we consider two model Hamiltonians in the mean-field approximation; the first is the standard 'one-site' model where quantum tunnelling is approximated entirely using mean-field terms; the second 'two-site' model explicitly includes tunnelling between two adjacent sites while treating tunnelling with other neighbouring sites using the mean-field approximation. The ground state is determined by minimizing the classical energy functional subject to quantum mechanical constraints, which take the form of uncertainty relations. For each model Hamiltonian, we compare the ground state results from the Q-function method with the exact numerical solution. The results from the Q-function method, which are easy to compute, give a good qualitative description of the main features of the Bose–Hubbard model including the superfluid to Mott insulator. We find the quantum mechanical constraints dominate the problem and show there are some limitations of the method particularly in the weak lattice regime.

Journal of Physics B Atomic Molecular and Optical Physics•Sep 15, 2004•11 citations
The zero temperature properties of the generalized Bose–Hubbard model including three-body interactions are studied on a mean-field level. We obtain analytical results using the so-called perturbative mean-field method and more detailed numerical results using the Gutzwiller product state variational ansatz. These two approaches yield equivalent results which compare well on a qualitative level with recent exact results obtained in the literature.
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)].
We investigate the mean-field phase diagram of the Bose-Hubbard model with infinite-range interactions in two dimensions. This model describes ultracold bosonic atoms confined by a two-dimensional optical lattice and dispersively coupled to a cavity mode with the same wavelength as the lattice. We determine the ground-state phase diagram for a grand-canonical ensemble by means of analytical and numerical methods. Our results mostly agree with the ones reported in Dogra et al. [N. Dogra, F. Brennecke, S. D. Huber, and T. Donner, Phys. Rev. A 94, 023632 (2016)], and have a remarkable qualitative agreement with the quantum Monte Carlo phase diagrams of Flottat et al. [T. Flottat, L. de Forges de Parny, F. H\'ebert, V. G. Rousseau, and G. G. Batrouni, Phys. Rev. B 95, 144501 (2017)]. The salient differences concern the stability of the supersolid phases, which we discuss in detail. Finally, we discuss differences and analogies between the ground-state properties of all-connected bosons with the ones predicted for repulsively interacting dipolar bosons in two dimensions.
This chapter reviews various theoretical methods that can be applied to investigate Bose–Hubbard models. In particular, it discusses the Bogolyubov method, strong coupling expansion, the perturbative mean field approach and the Gutzwiller method, exact diagonalization, quantum Monte Carlo methods, semi-classical phase space methods, and methods specifics for 1D (Wigner-Jordan transformation, Bethe ansatz, bosonization). The chapter end with a discussion about numerical renormalization approaches in 1D (DMRG, MPS) and 2D (PEPS; MERA).
We present a phase-space method for the Bose–Hubbard model based on the Q-function representation. In particular, we consider two model Hamiltonians in the mean-field approximation; the first is the standard 'one-site' model where quantum tunnelling is approximated entirely using mean-field terms; the second 'two-site' model explicitly includes tunnelling between two adjacent sites while treating tunnelling with other neighbouring sites using the mean-field approximation. The ground state is determined by minimizing the classical energy functional subject to quantum mechanical constraints, which take the form of uncertainty relations. For each model Hamiltonian, we compare the ground state results from the Q-function method with the exact numerical solution. The results from the Q-function method, which are easy to compute, give a good qualitative description of the main features of the Bose–Hubbard model including the superfluid to Mott insulator. We find the quantum mechanical constraints dominate the problem and show there are some limitations of the method particularly in the weak lattice regime.