We study, by means of exact-diagonalization techniques, the ground state of a few-fermion system with strong short-range repulsive interactions trapped by a harmonic potential in one spatial dimension. Even when the ground-state density profile displays, at strong coupling, very well pronounced Wigner oscillations with a $4{k}_{\mathrm{F}}$ periodicity, the pair-correlation function does not show any signature of Wigner-molecule-type correlations. For the sake of comparison, we present also numerical results for few-electron systems with Coulomb interactions, demonstrating that their ground state at strong coupling is, on the contrary, a Wigner molecule.We study, by means of exact-diagonalization techniques, the ground state of a few-fermion system with strong short-range repulsive interactions trapped by a harmonic potential in one spatial dimension. Even when the ground-state density profile displays, at strong coupling, very well pronounced Wigner oscillations with a $4{k}_{\mathrm{F}}$ periodicity, the pair-correlation function does not show any signature of Wigner-molecule-type correlations. For the sake of comparison, we present also numerical results for few-electron systems with Coulomb interactions, demonstrating that their ground state at strong coupling is, on the contrary, a Wigner molecule.

arXiv:1202.3284Physical Review BAug 7, 201231 citations

Ground state of an interacting boson system

Eugene Feenberg

Annals of PhysicsMay 1, 197443 citations

Strongly interacting Bose–Fermi mixtures in one dimension

Haiping Hu, Liming Guan, Shu Chen

We study one-dimensional (1D) strongly interacting Bose–Fermi mixtures by both the exact Bethe-ansatz method and variational perturbation theory within the degenerate ground state subspace of the system in the infinitely repulsive limit. Based on the exact solution of the 1D Bose–Fermi gas with equal boson–boson and boson–fermion interaction strengths, we demonstrate that the ground state energy is degenerate for different Bose–Fermi configurations and the degeneracy is lifted when the interaction deviates the infinitely interacting limit. We then show that the ground properties in the strongly interacting regime can be well characterized by using the variational perturbation method within the degenerate ground state subspace, which can be applied to deal with more general cases with anisotropic interactions and in external traps. Our results indicate that the total ground-state density profile in the strongly repulsive regime behaves like the polarized non-interacting fermions, whereas the density distributions of bosons and fermions display different properties for different Bose–Fermi configurations and are sensitive to the anisotropy of interactions.We study one-dimensional (1D) strongly interacting Bose–Fermi mixtures by both the exact Bethe-ansatz method and variational perturbation theory within the degenerate ground state subspace of the system in the infinitely repulsive limit. Based on the exact solution of the 1D Bose–Fermi gas with equal boson–boson and boson–fermion interaction strengths, we demonstrate that the ground state energy is degenerate for different Bose–Fermi configurations and the degeneracy is lifted when the interaction deviates the infinitely interacting limit. We then show that the ground properties in the strongly interacting regime can be well characterized by using the variational perturbation method within the degenerate ground state subspace, which can be applied to deal with more general cases with anisotropic interactions and in external traps. Our results indicate that the total ground-state density profile in the strongly repulsive regime behaves like the polarized non-interacting fermions, whereas the density distributions of bosons and fermions display different properties for different Bose–Fermi configurations and are sensitive to the anisotropy of interactions.

arXiv:1510.03369New Journal of PhysicsFeb 5, 201630 citations

Ground state of an interacting boson system

Annals of PhysicsApr 1, 19742 citations

Analytical and numerical studies of Bose–Fermi mixtures in a one-dimensional harmonic trap

Amin S. Dehkharghani, F. F. Bellotti, Nikolaj Thomas Zinner

Abstract In this paper we study a mixed system of bosons and fermions with up to six particles in total. All particles are assumed to have the same mass. The two-body interactions are repulsive and are assumed to have equal strength in both the Bose–Bose and the Fermi–Boson channels. The particles are confined externally by a harmonic oscillator one-body potential. For the case of four particles, two identical fermions and two identical bosons, we focus on the strongly interacting regime and analyze the system using both an analytical approach and density matrix renormalization group calculations using a discrete version of the underlying continuum Hamiltonian. This provides us with insight into both the ground state and the manifold of excited states that are almost degenerate for large interaction strength. Our results show great variation in the density profiles for bosons and fermions in different states for strongly interacting mixtures. By moving to slightly larger systems, we find that the ground state of balanced mixtures of four to six particles tends to separate bosons and fermions for strong (repulsive) interactions. On the other hand, in imbalanced Bose–Fermi mixtures we find pronounced odd–even effects in systems of five particles. These few-body results suggest that question of phase separation in one-dimensional confined mixtures are very sensitive to system composition, both for the ground state and the excited states.Abstract In this paper we study a mixed system of bosons and fermions with up to six particles in total. All particles are assumed to have the same mass. The two-body interactions are repulsive and are assumed to have equal strength in both the Bose–Bose and the Fermi–Boson channels. The particles are confined externally by a harmonic oscillator one-body potential. For the case of four particles, two identical fermions and two identical bosons, we focus on the strongly interacting regime and analyze the system using both an analytical approach and density matrix renormalization group calculations using a discrete version of the underlying continuum Hamiltonian. This provides us with insight into both the ground state and the manifold of excited states that are almost degenerate for large interaction strength. Our results show great variation in the density profiles for bosons and fermions in different states for strongly interacting mixtures. By moving to slightly larger systems, we find that the ground state of balanced mixtures of four to six particles tends to separate bosons and fermions for strong (repulsive) interactions. On the other hand, in imbalanced Bose–Fermi mixtures we find pronounced odd–even effects in systems of five particles. These few-body results suggest that question of phase separation in one-dimensional confined mixtures are very sensitive to system composition, both for the ground state and the excited states.

arXiv:1703.01836Journal of Physics B Atomic Molecular and Optical PhysicsJun 19, 201722 citations

4{k}_{\mathrm{F}}

periodicity, the pair-correlation function does not show any signature of Wigner-molecule-type correlations. For the sake of comparison, we present also numerical results for few-electron systems with Coulomb interactions, demonstrating that their ground state at strong coupling is, on the contrary, a Wigner molecule.