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arXiv:1511.09361 · Physical Review A

Ground state of the two-dimensional attractive Fermi gas: Essential properties from few to many body

Lukas Rammelmüller, William J. Porter, Joaquín E. Drut

Published Mar 21, 2016• 25 citations
arXivHTMLPDF

Abstract

We calculate the ground-state properties of unpolarized two-dimensional attractive fermions in the range from few to many particles. Using first-principles lattice Monte Carlo methods, we determine the ground-state energy, Tan's contact, momentum distribution, and single-particle correlation function. We investigate those properties for systems of $N=4,8,\ensuremath{\cdots},40$ particles and for a wide range of attractive couplings. As the attractive coupling is increased, the thermodynamic limit is reached at progressively lower $N$ due to the dominance of the two-body sector. At large momenta $k$, the momentum distribution displays the expected ${k}^{\ensuremath{-}4}$ behavior, but its onset shifts from $k\ensuremath{\simeq}1.8{k}_{F}^{}$ at weak coupling towards higher $k$ at strong coupling.

DOI
10.1103/physreva.93.033639

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We calculate the ground-state properties of unpolarized two-dimensional attractive fermions in the range from few to many particles. Using first-principles lattice Monte Carlo methods, we determine the ground-state energy, Tan's contact, momentum distribution, and single-particle correlation function. We investigate those properties for systems of N=4,8,\ensuremath⋯,40N=4,8,\ensuremath{\cdots},40N=4,8,\ensuremath⋯,40 particles and for a wide range of attractive couplings. As the attractive coupling is increased, the thermodynamic limit is reached at progressively lower NNN due to the dominance of the two-body sector. At large momenta kkk, the momentum distribution displays the expected k\ensuremath−4{k}^{\ensuremath{-}4}k\ensuremath−4 behavior, but its onset shifts from k\ensuremath≃1.8kFk\ensuremath{\simeq}1.8{k}_{F}^{}k\ensuremath≃1.8kF​ at weak coupling towards higher kkk at strong coupling.
Using the lattice Monte Carlo method, we compute the energy and Tan's contact in the ground state as well as the first excited state of few- to many-fermion systems in a one-dimensional periodic box. We focus on unpolarized systems of N=4,6,...,12N=4,6,...,12N=4,6,...,12 particles, with a zero-range interaction, and a wide range of attractive couplings. In addition, we provide extrapolations to the infinite-volume and thermodynamic limits.
Using the lattice Monte Carlo method, we compute the energy and Tan's contact in the ground state as well as the first excited state of few- to many-fermion systems in a one-dimensional periodic box. We focus on unpolarized systems of N = 4,6,...,12 particles, with a zero-range interaction, and a wide range of attractive couplings. In addition, we determine the critical coupling for bound-state formation and provide extrapolations to the infinite volume and thermodynamic limits. For the latter, we find agreement with previous calculations based on the Bethe ansatz.
Motivated by the realization of hard-wall boundary conditions in experiments with ultracold atoms, we investigate the ground-state properties of spin-1/2 fermions with attractive interactions in a one-dimensional box.We use lattice Monte Carlo methods to determine essential quantities like the energy, which we compute as a function of coupling strength and particle number in the regime from few to many particles.Many-fermion systems bound by hard walls display non-trivial density profiles characterized by so-called Friedel oscillations (which are similar to those observed in harmonic traps).In non-interacting systems, the characteristic length scale of the oscillations is set by (2k F ) -1 , where k F is the Fermi momentum, while repulsive interactions tend to generate Wignercrystal oscillations of period (4k F ) -1 .Based on the non-interacting result, we find a remarkably simple parametrization of the density profiles of the attractively interacting case, which we generalize to the one-body density matrix.While the total momentum is not a conserved quantity in the presence of hard walls, the magnitude of the momentum does provide a good quantum number.We are therefore able to provide a detailed characterization of the (quasi-)momentum distribution, which displays rather robust discontinuity at the Fermi surface.In addition, we determine the spatially varying on-site density-density correlation, which in turn yields Tan's contact density and, upon integration, Tan's contact.As is well known, the latter fully determines the short-range correlations and plays a crucial role in a multitude of equilibrium and non-equilibrium sum rules.
Abstract Motivated by the realization of hard-wall boundary conditions in experiments with ultracold atoms, we investigate the ground-state properties of spin-1/2 fermions with attractive interactions in a one-dimensional box. We use lattice Monte Carlo methods to determine essential quantities like the energy, which we compute as a function of coupling strength and particle number in the regime from few to many particles. Many-fermion systems bound by hard walls display non-trivial density profiles characterized by so-called Friedel oscillations (which are similar to those observed in harmonic traps). In non-interacting systems, the characteristic length scale of the oscillations is set by ( 2 k F ) − 1 , where k F is the Fermi momentum, while repulsive interactions tend to generate Wigner-crystal oscillations of period ( 4 k F ) − 1 . Based on the non-interacting result, we find a remarkably simple parametrization of the density profiles of the attractively interacting case, which we generalize to the one-body density matrix. While the total momentum is not a conserved quantity in the presence of hard walls, the magnitude of the momentum does provide a good quantum number. We are therefore able to provide a detailed characterization of the (quasi-)momentum distribution, which displays rather robust discontinuity at the Fermi surface. In addition, we determine the spatially varying on-site density–density correlation, which in turn yields Tan’s contact density and, upon integration, Tan’s contact. As is well known, the latter fully determines the short-range correlations and plays a crucial role in a multitude of equilibrium and non-equilibrium sum rules.
We study harmonically trapped, unpolarized fermion systems with attractive interactions in two spatial dimensions with spin degeneracies Nf=2{N}_{f}^{}=2Nf​=2 and 4 and N/Nf=1,3,5N/{N}_{f}^{}=1,\phantom{\rule{0.28em}{0ex}}3,\phantom{\rule{0.28em}{0ex}}5N/Nf​=1,3,5, and 7 particles per flavor. We carry out our calculations using our recently proposed quantum Monte Carlo method on a nonuniform lattice. We report on the ground-state energy and contact for a range of couplings, as determined by the binding energy of the two-body system, and show explicitly how the physics of the Nf{N}_{f}Nf​-body sector dominates as the coupling is increased.
Exact calculations are performed on the two-dimensional strongly interacting unpolarized uniform Fermi gas with a zero-range attractive interaction. Two auxiliary-field approaches are employed which accelerate the sampling of imaginary-time paths using BCS trial wave functions and a force bias technique. Their combination enables calculations on large enough lattices to reliably compute ground-state properties in the thermodynamic limit. An equation of state is obtained with a parametrization provided, which can serve as a benchmark and allow accurate comparisons with experiments. The pressure, contact parameter, and condensate fraction are determined systematically vs kFa{k}_{F}akF​a. The momentum distribution, pairing correlation, and the structure of the pair wave function are computed. The use of force bias to accelerate the Metropolis sampling of auxiliary fields in determinantal approaches is discussed.