Drops containing 20 to 240 atoms of Bose liquid $^{4}\mathrm{He}$ and Fermi liquid $^{3}\mathrm{He}$ are studied by variational Monte Carlo methods as simple examples of correlated inhomogeneous quantum systems. In the present work we report wave functions of natural, quasiparticle, and mean-field orbitals in these drops. The wave functions of natural orbitals are determined by diagonalizing the one-particle density matrix. The condensate fraction and wave function in the Bose-liquid drops are calculated. The quasihole states are defined in the spirit of Landau's theory, and their wave functions are calculated from the overlaps between states containing N and N-1 atoms. In Bose-liquid drops the wave function of the quasihole orbital is similar to that of the condensate; however, in Fermi-liquid drops the quasihole wave functions are different from those of natural or mean-field orbitals. We find that a simple local-density approximation provides an accurate relation between the mean-field and quasihole wave functions for both Bose- and Fermi-liquid drops. The wave functions of natural orbitals are very localized and simple methods to construct them from mean-field wave functions are also discussed. The momentum distributions of atoms in the drops are calculated and compared with those of extended liquids. The deviations of the momentum distributions from mean-field distributions are also discussed.Drops containing 20 to 240 atoms of Bose liquid $^{4}\mathrm{He}$ and Fermi liquid $^{3}\mathrm{He}$ are studied by variational Monte Carlo methods as simple examples of correlated inhomogeneous quantum systems. In the present work we report wave functions of natural, quasiparticle, and mean-field orbitals in these drops. The wave functions of natural orbitals are determined by diagonalizing the one-particle density matrix. The condensate fraction and wave function in the Bose-liquid drops are calculated. The quasihole states are defined in the spirit of Landau's theory, and their wave functions are calculated from the overlaps between states containing N and N-1 atoms. In Bose-liquid drops the wave function of the quasihole orbital is similar to that of the condensate; however, in Fermi-liquid drops the quasihole wave functions are different from those of natural or mean-field orbitals. We find that a simple local-density approximation provides an accurate relation between the mean-field and quasihole wave functions for both Bose- and Fermi-liquid drops. The wave functions of natural orbitals are very localized and simple methods to construct them from mean-field wave functions are also discussed. The momentum distributions of atoms in the drops are calculated and compared with those of extended liquids. The deviations of the momentum distributions from mean-field distributions are also discussed.

Physical review. B, Condensed matterApr 1, 1988115 citations

Quasiparticle energy and interaction in a normal electron liquid

Sudhakar Yarlagadda, Gabriele F. Giuliani

Solid State CommunicationsFeb 1, 198915 citations

Spatial fluctuations of spin and orbital nature in the two-orbital Hubbard model

Tomoko Kita, Takuma Ohashi, Sei-ichiro Suga

We investigate the quasiparticle dynamics in the two-orbital Hubbard model on the square lattice at quarter filling by means of the cellular dynamical mean-field theory. We show that the Fermi-liquid state is stabilized up to the large Hubbard interactions in the symmetric case without Hund's coupling, and find the heavy quasiparticles around the metal-insulator boundary. It is elucidated that Hund's coupling enhances the antiferro-orbital correlations, which give rise to the pseudogap behavior in the single-particle excitations. We also find the nonmonotonic temperature dependence in the quasiparticle dynamics for intermediate strength of Hund's coupling, and clarify that it is caused by the competition between the Fermi-liquid formation and the antiferro-orbital fluctuations.We investigate the quasiparticle dynamics in the two-orbital Hubbard model on the square lattice at quarter filling by means of the cellular dynamical mean-field theory. We show that the Fermi-liquid state is stabilized up to the large Hubbard interactions in the symmetric case without Hund's coupling, and find the heavy quasiparticles around the metal-insulator boundary. It is elucidated that Hund's coupling enhances the antiferro-orbital correlations, which give rise to the pseudogap behavior in the single-particle excitations. We also find the nonmonotonic temperature dependence in the quasiparticle dynamics for intermediate strength of Hund's coupling, and clarify that it is caused by the competition between the Fermi-liquid formation and the antiferro-orbital fluctuations.

arXiv:0812.4019Physical Review BJun 24, 200911 citations

Natural and Dyson orbitals in small helium drops

N. K. Timofeyuk

Abstract The natural and Dyson orbitals are studied for small helium drops comprising 5 to 20 helium atoms interacting via a soft two-body Gaussian potential. The wave functions of these drops have been obtained in the hyperspherical cluster model (HCM) which provides a correct description of the single-particle behavior at large separations from the system. The natural orbitals are obtained from diagonalization of the nonlocal one-body density matrix, while Dyson orbitals are constructed by the direct overlap of the wave functions of two drops differing by one boson. This overlap converges with an increasing basis of the HCM. The shapes and occupancies of the natural orbitals, as well as their link to Dyson overlap and evolution with increasing number of atoms, are discussed. Both natural and Dyson orbitals can be used to represent the density of the system. However, the natural orbital representation is demonstrated to be superior. With increasing boson numbers the difference between Dyson and natural orbitals becomes less prominent and is expected to disappear in infinitely large systems of identical bosons.Abstract The natural and Dyson orbitals are studied for small helium drops comprising 5 to 20 helium atoms interacting via a soft two-body Gaussian potential. The wave functions of these drops have been obtained in the hyperspherical cluster model (HCM) which provides a correct description of the single-particle behavior at large separations from the system. The natural orbitals are obtained from diagonalization of the nonlocal one-body density matrix, while Dyson orbitals are constructed by the direct overlap of the wave functions of two drops differing by one boson. This overlap converges with an increasing basis of the HCM. The shapes and occupancies of the natural orbitals, as well as their link to Dyson overlap and evolution with increasing number of atoms, are discussed. Both natural and Dyson orbitals can be used to represent the density of the system. However, the natural orbital representation is demonstrated to be superior. With increasing boson numbers the difference between Dyson and natural orbitals becomes less prominent and is expected to disappear in infinitely large systems of identical bosons.

arXiv:2605.12315Journal of Physics B Atomic Molecular and Optical PhysicsMay 15, 20250 citations

Quasiparticle self-energy of an electron liquid

George Simion, Reza Asgari, B. Davoudi +4 more

APSMar 1, 20040 citations

Drops containing 20 to 240 atoms of Bose liquid

^{4}\mathrm{He}

and Fermi liquid

^{3}\mathrm{He}

are studied by variational Monte Carlo methods as simple examples of correlated inhomogeneous quantum systems. In the present work we report wave functions of natural, quasiparticle, and mean-field orbitals in these drops. The wave functions of natural orbitals are determined by diagonalizing the one-particle density matrix. The condensate fraction and wave function in the Bose-liquid drops are calculated. The quasihole states are defined in the spirit of Landau's theory, and their wave functions are calculated from the overlaps between states containing N and N-1 atoms. In Bose-liquid drops the wave function of the quasihole orbital is similar to that of the condensate; however, in Fermi-liquid drops the quasihole wave functions are different from those of natural or mean-field orbitals. We find that a simple local-density approximation provides an accurate relation between the mean-field and quasihole wave functions for both Bose- and Fermi-liquid drops. The wave functions of natural orbitals are very localized and simple methods to construct them from mean-field wave functions are also discussed. The momentum distributions of atoms in the drops are calculated and compared with those of extended liquids. The deviations of the momentum distributions from mean-field distributions are also discussed.