Ab initio nuclear physics tackles the problem of strongly interacting four-component fermions. The same setting could foreseeably be probed experimentally in ultracold atomic systems, where two- and three-component experiments have led to major breakthroughs in recent years. Both due to the problem's inherent interest and as a pathway to nuclear physics, in this Letter we study four-component fermions at unitarity via the use of quantum Monte Carlo methods. We explore novel forms of the trial wave function and find one which leads to a ground state of the eight-particle system whose energy is almost equal to that of two four-particle systems. We investigate the clustering properties involved and also extrapolate to the zero-range limit. In addition to being experimentally testable, our results impact the prospects of developing nuclear physics as a perturbation around the unitary limit.
Ab initio nuclear physics tackles the problem of strongly interacting four-component fermions. The same setting could foreseeably be probed experimentally in ultracold atomic systems, where two- and three-component experiments have led to major breakthroughs in recent years. Both due to the problem's inherent interest and as a pathway to nuclear physics, in this Letter we study four-component fermions at unitarity via the use of quantum Monte Carlo methods. We explore novel forms of the trial wave function and find one which leads to a ground state of the eight-particle system whose energy is almost equal to that of two four-particle systems. We investigate the clustering properties involved and also extrapolate to the zero-range limit. In addition to being experimentally testable, our results impact the prospects of developing nuclear physics as a perturbation around the unitary limit.
The unitarity limit describes interacting particles where the range of the interaction is zero and the scattering length is infinite. We present precision benchmark calculations for two-component fermions at unitarity using three different ab initio methods: Hamiltonian lattice formalism using iterated eigenvector methods, Euclidean lattice formalism with auxiliary-field projection Monte Carlo methods, and continuum diffusion Monte Carlo methods with fixed and released nodes. We have calculated the ground-state energy of the unpolarized four-particle system in a periodic cube as a dimensionless fraction of the ground-state energy for the noninteracting system. We obtain values of 0.211(2) and 0.210(2) using two different Hamiltonian lattice representations, 0.206(9) using Euclidean lattice formalism, and an upper bound of 0.212(2) from fixed-node diffusion Monte Carlo methods. Released-node calculations starting from the fixed-node result yield a decrease of less than 0.002 over a propagation of $0.4{E}_{F}^{\ensuremath{-}1}$ in Euclidean time, where EF is the Fermi energy. We find good agreement among all three ab initio methods.
Quantum Monte Carlo methods have proven to be valuable in the study of strongly correlated quantum systems, particularly nuclear physics and cold atomic gases. Historically, such ab initio simulations have been used to study properties of light nuclei, including spectra and form factors, low-energy scattering, and high-momentum properties including inclusive scattering and one- and two-body momentum distributions. More recently they have been used to study the properties of homogeneous and inhomogeneous neutron matter and cold atomic gases. There are close analogies between these seemingly diverse systems, including the equation of state, superfluid pairing, and linear response to external probes. In this paper, we compare and contrast results found in nuclear and cold atom physics. We show updated lattice results for the energy of the homogeneous unitary Fermi gas and comparisons with neutron matter, as well as for the dependence of the cold atom energy on the mass ratio between paired particles, which yields insights on the structure of the ground state. We also provide new lattice and continuum results for the harmonically trapped unitary gas, again comparing neutron matter and cold atoms.
Quantum Monte Carlo methods have proven to be valuable in the study of strongly correlated quantum systems, particularly nuclear physics and cold atomic gases. Historically, such ab initio simulations have been used to study properties of light nuclei, including spectra and form factors, low-energy scattering, and high-momentum properties including inclusive scattering and one- and two-body momentum distributions. More recently they have been used to study the properties of homogeneous and inhomogeneous neutron matter and cold atomic gases. There are close analogies between these seemingly diverse systems, including the equation of state, superfluid pairing, and linear response to external probes. In this paper, we compare and contrast results found in nuclear and cold atom physics. We show updated lattice results for the energy of the homogeneous unitary Fermi gas and comparisons with neutron matter, as well as for the dependence of the cold atom energy on the mass ratio between paired particles, which yields insights on the structure of the ground state. We also provide new lattice and continuum results for the harmonically trapped unitary gas, again comparing neutron matter and cold atoms. Quantum Monte Carlo methods1), 2) have been proven very valuable in study-ing a host of strongly correlated quantum systems, including solid and liquid He-lium,3), 4), 5), 6) electronic systems,7), 8) light nuclei9), 10), 11) and more recently neutron
We calculate the ground-state properties of an unpolarized two-component Fermi gas with the aid of the diffusion quantum Monte Carlo (DMC) methods. Using an extrapolation to the zero effective range of the attractive two-particle interaction, we find E/Efree in the unitary limit to be 0.212(2), 0.407(2), 0.409(3), and 0.398(3) for 4, 14, 38, and 66 atoms, respectively. Our calculations indicate that the dependence of the total energy on the effective range of the interaction Reff is sizable and the extrapolation to Reff=0 is therefore important for reaching the true unitary limit. To test the quality of nodal surfaces and to estimate the impact of the fixed-node approximation, we perform released-node DMC calculations for 4 and 14 atoms. Analysis of the released-node and the fixed-node results suggests that the main sources of the fixed-node errors are long-range correlations, which are difficult to sample in the released-node approaches due to the fast growth of the bosonic noise. Besides energies, we evaluate the two-body density matrix and the condensate fraction. We find that the condensate fraction for the 66-atom system converges to 0.56(1) after the extrapolation to the zero interaction range.
In recent years Quantum Monte Carlo techniques provided to be a valuable tool to study strongly interacting Fermi gases at zero temperature. We have used QMC methods to investigate several properties of the two-components Fermi gas at unitarity and in the BCS-BEC crossover, both with equal and unequal masses corresponding to the Li – K Fermi mixture. In this paper we present several recent QMC results, including the energy at zero and finite effective range, the contact parameter and the static structure factor, which, at low momentum, depends strongly on the phonons in the unitary Fermi gas.
Abstract. In recent years Quantum Monte Carlo techniques provided to be a valuable tool to study strongly interacting Fermi gases at zero temperature. We have used QMC methods to investigate several properties of the two-components Fermi gas at unitarity and in the BCS-BEC crossover, both with equal and unequal masses corresponding to the Li−K Fermi mixture. In this paper we present several recent QMC results, including the energy at zero and finite effective range, the contact parameter and the static structure factor, which, at low momentum, depends strongly on the phonons in the unitary Fermi gas. 1.