We calculate the ground state energies of a system of two dipolar fermions trapped in a harmonic oscillator potential. The dipoles are assumed to be aligned parallel to each other. We perform the calculations of ground state energy as a function of strength of interaction between two fermions by employing variational method with Hylleraas-like explicitly correlated wave function. Furthermore, we perform calculations of ground state energy within Hartree-Fock approximation and the magnitude of correlation energy is estimated by subtracting these results from the corresponding wave function based results. We also carry out calculations of ground state energies within the realm of density functional theory by using recently reported expressions for exchange and correlation energies under local density approximation. By comparing correlated wave function based results with those obtained using density functional theory approach we examine the role of fermion-fermion correlation and assess the accuracy of local density approximation based expression for the correlation energy functional.We calculate the ground state energies of a system of two dipolar fermions trapped in a harmonic oscillator potential. The dipoles are assumed to be aligned parallel to each other. We perform the calculations of ground state energy as a function of strength of interaction between two fermions by employing variational method with Hylleraas-like explicitly correlated wave function. Furthermore, we perform calculations of ground state energy within Hartree-Fock approximation and the magnitude of correlation energy is estimated by subtracting these results from the corresponding wave function based results. We also carry out calculations of ground state energies within the realm of density functional theory by using recently reported expressions for exchange and correlation energies under local density approximation. By comparing correlated wave function based results with those obtained using density functional theory approach we examine the role of fermion-fermion correlation and assess the accuracy of local density approximation based expression for the correlation energy functional.

arXiv:1410.2078Oct 8, 20141 citation

The kinetic-energy functional of a one-dimensional system of fermions

V.Iu. Kolmanovich, I. M. Reznik

Soviet physics. DokladyJun 1, 19810 citations

BEC-BCS crossover of a trapped two-component Fermi gas with unequal masses

J. von Stecher, Chris H. Greene, D. Blume

We determine the energetically lowest-lying states in the BEC-BCS crossover regime of $s$ -wave interacting two-component Fermi gases under harmonic confinement by solving the many-body Schr\"odinger equation using two distinct approaches. Essentially exact basis set expansion techniques are applied to determine the energy spectrum of systems with $N=4$ fermions. Fixed-node diffusion Monte Carlo methods are applied to systems with up to $N=20$ fermions, and a discussion of different guiding functions used in the Monte Carlo approach to impose the proper symmetry of the fermionic system is presented. The energies are calculated as a function of the $s$ -wave scattering length ${a}_{s}$ for $N=2--20$ fermions and different mass ratios $\ensuremath{\kappa}$ of the two species. On the Bose-Einstein condensate (BEC) and BCS sides, our energies agree with analytically determined first-order correction terms. We extract the scattering length and the effective range of the dimer-dimer system up to $\ensuremath{\kappa}=20$. Our energies for the strongly interacting trapped system in the unitarity regime show essentially no shell structure, and are well described by a simple expression whose functional form can be derived using the local density approximation, with one or two parameters. The universal parameter $\ensuremath{\xi}$ for the trapped system for various $\ensuremath{\kappa}$ is determined, and comparisons with results for the homogeneous system are presented.We determine the energetically lowest-lying states in the BEC-BCS crossover regime of $s$-wave interacting two-component Fermi gases under harmonic confinement by solving the many-body Schr\"odinger equation using two distinct approaches. Essentially exact basis set expansion techniques are applied to determine the energy spectrum of systems with $N=4$ fermions. Fixed-node diffusion Monte Carlo methods are applied to systems with up to $N=20$ fermions, and a discussion of different guiding functions used in the Monte Carlo approach to impose the proper symmetry of the fermionic system is presented. The energies are calculated as a function of the $s$-wave scattering length ${a}_{s}$ for $N=2--20$ fermions and different mass ratios $\ensuremath{\kappa}$ of the two species. On the Bose-Einstein condensate (BEC) and BCS sides, our energies agree with analytically determined first-order correction terms. We extract the scattering length and the effective range of the dimer-dimer system up to $\ensuremath{\kappa}=20$. Our energies for the strongly interacting trapped system in the unitarity regime show essentially no shell structure, and are well described by a simple expression whose functional form can be derived using the local density approximation, with one or two parameters. The universal parameter $\ensuremath{\xi}$ for the trapped system for various $\ensuremath{\kappa}$ is determined, and comparisons with results for the homogeneous system are presented.

arXiv:0705.0671Physical Review ANov 15, 200770 citations

Calculation of the two-body correlation function for Fermion systems

Stefano Fantoni, Sergio Rosati

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoJul 1, 197473 citations

The ground state energy of odd fermion systems

Judit Németh

Acta Physica Academiae Scientiarum HungaricaeApr 1, 19642 citations

Statistics of Two Kinds of Entangled Quantum Many-body Systems

Hua-Bi Zeng

In this paper, we show two kinds of entangled many body systems with special statistic properties. Firstly, an entangled fermions system with a pairwise entanglement between every two particles in the lowest energy energy level obeys the fractional statistics. As a check, for particle number N=2, N=3 and N=4, considering that any two fermions in the lowest Landau level are entangled in a proper way, the Laughlin wave function can be derived. The results reveals the explicit entanglement pattern of the Laughlin states. Secondly, we noticed that both Bose-Einstein statistics and Fermi-Dirac distributions are derived from computing the partial function of a free quantum many body system in a certain ensemble without considering entanglement. We extend the computation of the partial function to an entangled quantum many body system without interaction, in this system we assume that every particle in energy level $ε_i$ is entangled with a particle in the energy level $ε_{i+1}$ ( $i=1,3,5,...$ ) and also every particle in energy level $ε_i+1$ is entangled with a particle in the energy level $ε_{i}$ ( $i=1,3,5,...$ ), which indicates that the two energy level have the same number of particles. In the entangled system, we find that the partial function will be changed. As a results, both the Bose-Einstein Statics and the Fermi-Dirac distributions will be modified at finite temperature.In this paper, we show two kinds of entangled many body systems with special statistic properties. Firstly, an entangled fermions system with a pairwise entanglement between every two particles in the lowest energy energy level obeys the fractional statistics. As a check, for particle number N=2, N=3 and N=4, considering that any two fermions in the lowest Landau level are entangled in a proper way, the Laughlin wave function can be derived. The results reveals the explicit entanglement pattern of the Laughlin states. Secondly, we noticed that both Bose-Einstein statistics and Fermi-Dirac distributions are derived from computing the partial function of a free quantum many body system in a certain ensemble without considering entanglement. We extend the computation of the partial function to an entangled quantum many body system without interaction, in this system we assume that every particle in energy level $ε_i$ is entangled with a particle in the energy level $ε_{i+1}$ ($i=1,3,5,...$) and also every particle in energy level $ε_i+1$ is entangled with a particle in the energy level $ε_{i}$ ($i=1,3,5,...$), which indicates that the two energy level have the same number of particles. In the entangled system, we find that the partial function will be changed. As a results, both the Bose-Einstein Statics and the Fermi-Dirac distributions will be modified at finite temperature.

arXiv:1310.0331Sep 28, 20130 citations

We determine the energetically lowest-lying states in the BEC-BCS crossover regime of

s

-wave interacting two-component Fermi gases under harmonic confinement by solving the many-body Schr\"odinger equation using two distinct approaches. Essentially exact basis set expansion techniques are applied to determine the energy spectrum of systems with

N=4

fermions. Fixed-node diffusion Monte Carlo methods are applied to systems with up to

N=20

fermions, and a discussion of different guiding functions used in the Monte Carlo approach to impose the proper symmetry of the fermionic system is presented. The energies are calculated as a function of the

s

-wave scattering length

{a}_{s}

for

N=2--20

fermions and different mass ratios $\ensuremath{\kappa}$ of the two species. On the Bose-Einstein condensate (BEC) and BCS sides, our energies agree with analytically determined first-order correction terms. We extract the scattering length and the effective range of the dimer-dimer system up to $\ensuremath{\kappa}=20$. Our energies for the strongly interacting trapped system in the unitarity regime show essentially no shell structure, and are well described by a simple expression whose functional form can be derived using the local density approximation, with one or two parameters. The universal parameter $\ensuremath{\xi}$ for the trapped system for various $\ensuremath{\kappa}$ is determined, and comparisons with results for the homogeneous system are presented.

ε_i

is entangled with a particle in the energy level

ε_{i+1}

(

i=1,3,5,...

) and also every particle in energy level

ε_i+1

is entangled with a particle in the energy level

ε_{i}

(

i=1,3,5,...

), which indicates that the two energy level have the same number of particles. In the entangled system, we find that the partial function will be changed. As a results, both the Bose-Einstein Statics and the Fermi-Dirac distributions will be modified at finite temperature.