Continuing the diagrammatic analysis of the method of correlated basis functions (CBF) for the weakly interacting Bose gas, as reported in the preceding paper, we take off from the unperturbed problem, which is solved essentially by a variational method using a Jastrow correlating factor as the trial wave function. We compute low-order corrections to the unperturbed energy, using a set of correlated basis functions. It is found that the simplest second-order correction in the CBF accounts for all discrepancies (between the Hugenholtz-Pines theory and the unperturbed CBF calculation) which arise in the fourth order of the interaction strength $O({\ensuremath{\lambda}}^{4})$. It is also demonstrated indirectly that the Jastrow function sums rings and ladders at least up to $O({\ensuremath{\lambda}}^{5})$.Continuing the diagrammatic analysis of the method of correlated basis functions (CBF) for the weakly interacting Bose gas, as reported in the preceding paper, we take off from the unperturbed problem, which is solved essentially by a variational method using a Jastrow correlating factor as the trial wave function. We compute low-order corrections to the unperturbed energy, using a set of correlated basis functions. It is found that the simplest second-order correction in the CBF accounts for all discrepancies (between the Hugenholtz-Pines theory and the unperturbed CBF calculation) which arise in the fourth order of the interaction strength $O({\ensuremath{\lambda}}^{4})$. It is also demonstrated indirectly that the Jastrow function sums rings and ladders at least up to $O({\ensuremath{\lambda}}^{5})$.

Physical Review ANov 1, 197022 citations

THEORY OF CORRELATED BASIS FUNCTIONS

E. Krotscheck

Series on advances in quantum many-body theoryAug 1, 20029 citations

Correlated Basis Function Theory

Giampaolo Co’

UNITEXT for physicsJan 1, 20260 citations

Multicomponent correlated-basis-function method and its application to multilayered dipolar Bose gases

Michael Rader, Martin Hebenstreit, Robert E. Zillich

We present a method for calculating the dynamics of a bosonic mixture, the multicomponent correlated-basis-function (CBF) method. For a single component, CBF results for the excitation energies agree quite well with experimental results, even for highly correlated systems like $^{4}\mathrm{He}$ , and recent systematic improvements of CBF achieve perfect agreement. We give a full derivation of multicomponent CBF, and apply the method to a dipolar Bose gas cut into two-dimensional layers by a deep optical lattice, with coupling between layers due to the long-ranged dipole-dipole interaction. We consider the case of strong coupling, leading to large positive interlayer correlations. We calculate the spectrum for a system of eight layers and show that the strong coupling can lead to a simpler spectrum than in the uncoupled case, with a single peak carrying most of the spectral weight.We present a method for calculating the dynamics of a bosonic mixture, the multicomponent correlated-basis-function (CBF) method. For a single component, CBF results for the excitation energies agree quite well with experimental results, even for highly correlated systems like $^{4}\mathrm{He}$, and recent systematic improvements of CBF achieve perfect agreement. We give a full derivation of multicomponent CBF, and apply the method to a dipolar Bose gas cut into two-dimensional layers by a deep optical lattice, with coupling between layers due to the long-ranged dipole-dipole interaction. We consider the case of strong coupling, leading to large positive interlayer correlations. We calculate the spectrum for a system of eight layers and show that the strong coupling can lead to a simpler spectrum than in the uncoupled case, with a single peak carrying most of the spectral weight.

arXiv:1611.04757Physical Review AMar 24, 20176 citations

Coupled-cluster many-body theory in a correlated basis

E. Krotscheck, Hermann G. Kümmel, John G. Zabolitzky

The correlated-basis-functions method of Feenberg and the coupled-cluster formalism of Coester and K\"ummel are joined to form a new ground-state many-body method combining the advantages of both older methods and avoiding their disadvantages. From the point of view of the correlated-basis-functions method, coupled-cluster theory is used to sum the perturbation series partially to arbitrary order. From the point of view of the coupled-cluster method, correlated basis functions are used to take out the repulsive core of the two-body interaction in order to allow more efficient truncation schemes. It is found that powerful renormalizations are possible. Explicit equations are given for the two-body subsystems embodying generalized Bethe-Goldstone and random-phase equations summing, in the correlated basis, ladder and ring diagrams to arbitrary order.The correlated-basis-functions method of Feenberg and the coupled-cluster formalism of Coester and K\"ummel are joined to form a new ground-state many-body method combining the advantages of both older methods and avoiding their disadvantages. From the point of view of the correlated-basis-functions method, coupled-cluster theory is used to sum the perturbation series partially to arbitrary order. From the point of view of the coupled-cluster method, correlated basis functions are used to take out the repulsive core of the two-body interaction in order to allow more efficient truncation schemes. It is found that powerful renormalizations are possible. Explicit equations are given for the two-body subsystems embodying generalized Bethe-Goldstone and random-phase equations summing, in the correlated basis, ladder and ring diagrams to arbitrary order.

Physical Review ASep 1, 198030 citations

^{4}\mathrm{He}

, and recent systematic improvements of CBF achieve perfect agreement. We give a full derivation of multicomponent CBF, and apply the method to a dipolar Bose gas cut into two-dimensional layers by a deep optical lattice, with coupling between layers due to the long-ranged dipole-dipole interaction. We consider the case of strong coupling, leading to large positive interlayer correlations. We calculate the spectrum for a system of eight layers and show that the strong coupling can lead to a simpler spectrum than in the uncoupled case, with a single peak carrying most of the spectral weight.