© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:1111.4102 · Physical Review A

Multisite mean-field theory for cold bosonic atoms in optical lattices

Thomas Edward McIntosh, P. Pisarski, Robert J Gooding, E. Zaremba

Published Jul 16, 2012• 39 citations

Abstract

We present a detailed derivation of a multisite mean-field theory (MSMFT) used to describe the Mott-insulator to superfluid transition of bosonic atoms in optical lattices. The approach is based on partitioning the lattice into small clusters which are decoupled by means of a mean-field approximation. This approximation invokes local superfluid order parameters defined for each of the boundary sites of the cluster. The resulting MSMFT grand potential has a nontrivial topology as a function of the various order parameters. An understanding of this topology provides two different criteria for the determination of the Mott insulator superfluid phase boundaries. We apply this formalism to $d$-dimensional hypercubic lattices in one, two, and three dimensions and demonstrate the improvement in the estimation of the phase boundaries when MSMFT is utilized for increasingly larger clusters, with the best quantitative agreement found for $d=3$. The MSMFT is then used to examine a linear dimer chain in which the onsite energies within the dimer have an energy separation of $\ensuremath{\Delta}$. This system has a complicated phase diagram within the parameter space of the model, with many distinct Mott phases separated by superfluid regions.

DOI: 10.1103/physreva.86.013623

Related papers

Application of a multisite mean-field theory to the disordered Bose-Hubbard model

P. Pisarski, Ryan Matthew Jones, Robert J Gooding

We present a multisite formulation of mean-field theory applied to the disordered Bose-Hubbard model. In this approach the lattice is partitioned into clusters, each isolated cluster being treated exactly, with intercluster hopping being treated approximately. The theory allows for the possibility of a different superfluid order parameter at every site in the lattice, such as what has been used in previously published site-decoupled mean-field theories, but a multisite formulation also allows for the inclusion of spatial correlations allowing us, e.g., to calculate the correlation length (over the length scale of each cluster). We present our numerical results for a two-dimensional system. This theory is shown to produce a phase diagram in which the stability of the Mott-insulator phase is larger than that predicted by site-decoupled single-site mean-field theory. Two different methods are given for the identification of the Bose-glass--to--superfluid transition, one an approximation based on the behavior of the condensate fraction, and one that relies on obtaining the spatial variation of the order parameter correlation. The relation of our results to a recent proposal that both transitions are non-self-averaging is discussed.

arXiv:1103.4202•Physical Review A•May 6, 2011•32 citations

Quantum Phases of Cold Bosonic Atoms in an Optical Lattice with Inhomogeneous Atomic Interactions and Coexistence of Multi Phases*

Yanying Li, Jing-Min Hou

Abstract We study cold bosonic atoms on a two-dimensional inhomogeneous optical lattice with site-dependent atomic interactions. With the tight-binding approximation, we derive the extended Bose–Hubbard model. Base on the mean-field approximation, the ground states are solved by the exact diagonalization method. We calculate the mean-field order parameter and particle number density for the ground states. We find the coexistence of superfluid phase and Mott-insulator phase on the two-dimensional inhomogeneous optical lattice in appropriate parameter ranges.

Communications in Theoretical Physics•Apr 1, 2017•0 citations

Superfluid–Mott-insulator transition of spin-2 cold bosons in an optical lattice in a magnetic field

Shuo Jin, Jing-Min Hou, Bing-Hao Xie +2 more

The superfluid--Mott-insulator transition of spin-2 boson atoms with repulsive interaction in an optical lattice in a magnetic field is presented. By using the mean-field theory, the Mott ground states and phase diagrams of the superfluid--Mott-insulator transition at zero temperature are revealed. An applied magnetic field leads to splitting of some phase boundaries. For all the initial Mott ground states containing multiple spin components, different spin components take on different phase boundaries. It is found that in this system phase boundaries with different magnetization can be moved in different ways by changing only the intensity of the applied magnetic field.

arXiv:cond-mat/0312456•Physical Review A•Aug 19, 2004•9 citations

Quantum phase diagram of bosons in optical lattices

F. E. A. dos Santos, Axel Pelster

We work out two different analytical methods for calculating the boundary of the Mott-insulator--superfluid (MI-SF) quantum phase transition for scalar bosons in cubic optical lattices of arbitrary dimension at zero temperature which improve upon the seminal mean-field result. The first one is a variational method, which is inspired by variational perturbation theory, whereas the second one is based on the field-theoretic concept of effective potential. Within both analytical approaches we achieve a considerable improvement of the location of the MI-SF quantum phase transition for the first Mott lobe in excellent agreement with recent numerical results from quantum Monte Carlo simulations in two and three dimensions. Thus, our analytical results for the whole quantum phase diagram can be regarded as being essentially exact for all practical purposes.

arXiv:0806.2812•Physical Review A•Jan 15, 2009•87 citations

Improving mean-field theory for bosons in optical lattices via degenerate perturbation theory

M. Kübler, Felipe Taha Sant’Ana, F. E. A. dos Santos +1 more

The objective of this paper is the theoretical description of the Mott insulator to superfluid quantum phase transition of a Bose gas in an optical lattice. In former works the Rayleigh-Schr\"odinger perturbation theory was used within a mean-field approach, which yields partially nonphysical results since the degeneracy between two adjacent Mott lobes is not taken into account. In order to correct such nonphysical results we apply the Brillouin-Wigner perturbation theory to the mean-field approximation of the Bose-Hubbard model. Detailed explanations of how to use the Brillouin-Wigner theory are presented, including a graphical approach that allows one to efficiently keep track of the respective analytic terms. To prove the validity of this computation, the results are compared with other works. Besides the analytic calculation of the phase boundary from Mott insulator to superfluid phase, the condensate density is also determined by simultaneously solving two algebraic equations. The analytical and numerical results turn out to be physically meaningful and can cover a region of system parameters inaccessible until now. Our results are of particular interest provided a harmonic trap is added to the former calculations in a homogeneous system, in view of describing an experiment within the local-density approximation. Thus, the paper represents an essential preparatory work for determining the experimentally observed wedding cake structure of particle-density profile at both finite temperature and finite hopping.

arXiv:1804.08689•Physical Review A•Jun 10, 2019•11 citations

Multiband-driven superfluid-insulator transition of fermionic atoms in optical lattices: A dynamical mean-field-theory study

Takuji Higashiyama, Kensuke Inaba, Sei-ichiro Suga

The superfluid-insulator transition of fermionic atoms in optical lattices is investigated by two-site dynamical mean-field theory. It is shown that the Mott transition occurs as a result of multiband effects. The quasiparticle weight in the superfluid state decreases significantly as the system approaches the Mott transition point. By changing the interaction and the orbital splitting, we obtain the phase diagram at half filling. The numerical results are discussed in comparison with the effective boson model.

arXiv:0803.4347•Physical Review A•Apr 22, 2008•11 citations

We present a detailed derivation of a multisite mean-field theory (MSMFT) used to describe the Mott-insulator to superfluid transition of bosonic atoms in optical lattices. The approach is based on partitioning the lattice into small clusters which are decoupled by means of a mean-field approximation. This approximation invokes local superfluid order parameters defined for each of the boundary sites of the cluster. The resulting MSMFT grand potential has a nontrivial topology as a function of the various order parameters. An understanding of this topology provides two different criteria for the determination of the Mott insulator superfluid phase boundaries. We apply this formalism to

d

-dimensional hypercubic lattices in one, two, and three dimensions and demonstrate the improvement in the estimation of the phase boundaries when MSMFT is utilized for increasingly larger clusters, with the best quantitative agreement found for

d=3

. The MSMFT is then used to examine a linear dimer chain in which the onsite energies within the dimer have an energy separation of

\ensuremath{\Delta}

. This system has a complicated phase diagram within the parameter space of the model, with many distinct Mott phases separated by superfluid regions.

We present a multisite formulation of mean-field theory applied to the disordered Bose-Hubbard model. In this approach the lattice is partitioned into clusters, each isolated cluster being treated exactly, with intercluster hopping being treated approximately. The theory allows for the possibility of a different superfluid order parameter at every site in the lattice, such as what has been used in previously published site-decoupled mean-field theories, but a multisite formulation also allows for the inclusion of spatial correlations allowing us, e.g., to calculate the correlation length (over the length scale of each cluster). We present our numerical results for a two-dimensional system. This theory is shown to produce a phase diagram in which the stability of the Mott-insulator phase is larger than that predicted by site-decoupled single-site mean-field theory. Two different methods are given for the identification of the Bose-glass--to--superfluid transition, one an approximation based on the behavior of the condensate fraction, and one that relies on obtaining the spatial variation of the order parameter correlation. The relation of our results to a recent proposal that both transitions are non-self-averaging is discussed.

Abstract We study cold bosonic atoms on a two-dimensional inhomogeneous optical lattice with site-dependent atomic interactions. With the tight-binding approximation, we derive the extended Bose–Hubbard model. Base on the mean-field approximation, the ground states are solved by the exact diagonalization method. We calculate the mean-field order parameter and particle number density for the ground states. We find the coexistence of superfluid phase and Mott-insulator phase on the two-dimensional inhomogeneous optical lattice in appropriate parameter ranges.

The superfluid--Mott-insulator transition of spin-2 boson atoms with repulsive interaction in an optical lattice in a magnetic field is presented. By using the mean-field theory, the Mott ground states and phase diagrams of the superfluid--Mott-insulator transition at zero temperature are revealed. An applied magnetic field leads to splitting of some phase boundaries. For all the initial Mott ground states containing multiple spin components, different spin components take on different phase boundaries. It is found that in this system phase boundaries with different magnetization can be moved in different ways by changing only the intensity of the applied magnetic field.

We work out two different analytical methods for calculating the boundary of the Mott-insulator--superfluid (MI-SF) quantum phase transition for scalar bosons in cubic optical lattices of arbitrary dimension at zero temperature which improve upon the seminal mean-field result. The first one is a variational method, which is inspired by variational perturbation theory, whereas the second one is based on the field-theoretic concept of effective potential. Within both analytical approaches we achieve a considerable improvement of the location of the MI-SF quantum phase transition for the first Mott lobe in excellent agreement with recent numerical results from quantum Monte Carlo simulations in two and three dimensions. Thus, our analytical results for the whole quantum phase diagram can be regarded as being essentially exact for all practical purposes.

The objective of this paper is the theoretical description of the Mott insulator to superfluid quantum phase transition of a Bose gas in an optical lattice. In former works the Rayleigh-Schr\"odinger perturbation theory was used within a mean-field approach, which yields partially nonphysical results since the degeneracy between two adjacent Mott lobes is not taken into account. In order to correct such nonphysical results we apply the Brillouin-Wigner perturbation theory to the mean-field approximation of the Bose-Hubbard model. Detailed explanations of how to use the Brillouin-Wigner theory are presented, including a graphical approach that allows one to efficiently keep track of the respective analytic terms. To prove the validity of this computation, the results are compared with other works. Besides the analytic calculation of the phase boundary from Mott insulator to superfluid phase, the condensate density is also determined by simultaneously solving two algebraic equations. The analytical and numerical results turn out to be physically meaningful and can cover a region of system parameters inaccessible until now. Our results are of particular interest provided a harmonic trap is added to the former calculations in a homogeneous system, in view of describing an experiment within the local-density approximation. Thus, the paper represents an essential preparatory work for determining the experimentally observed wedding cake structure of particle-density profile at both finite temperature and finite hopping.

The superfluid-insulator transition of fermionic atoms in optical lattices is investigated by two-site dynamical mean-field theory. It is shown that the Mott transition occurs as a result of multiband effects. The quasiparticle weight in the superfluid state decreases significantly as the system approaches the Mott transition point. By changing the interaction and the orbital splitting, we obtain the phase diagram at half filling. The numerical results are discussed in comparison with the effective boson model.