Are smooth pseudopotentials a good choice for representing short-range interactions?

Abstract

When seeking a numerical representation of a quantum-mechanical multiparticle problem it is tempting to replace a singular short-range interaction by a smooth finite-range pseudopotential. Finite basis set expansions, e.g., in Fock space, are then guaranteed to converge exponentially. The need to faithfully represent the artificial length scale of the pseudopotential, however, places a costly burden on the basis set. Here we discuss scaling relations for the required size of the basis set and demonstrate the basis set convergence on the example of a two-dimensional system of few fermions with short-range s-wave interactions in a harmonic trapping potential. In particular we show that the number of harmonic-oscillator basis functions needed to reach a regime of exponential convergence for a Gaussian pseudopotential scales with the fourth power of the pseudopotential length scale, which can be improved to quadratic scaling when the basis functions are rescaled appropriately. Numerical examples for three fermions with up to a few hundred single-particle basis functions are presented and implications for the feasibility of accurate numerical multiparticle simulations of interacting ultracold-atom systems are discussed.

Pairing in two-dimensional Fermi gases with a coordinate-space potential

“…Experimentally, cold Fermi gases are produced in quasi-2D pancake-shape gas clouds [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Both preceding and following the experimental breakthroughs, a number of theoretical approaches have been brought to bear on the subject of lower-dimensional Fermi gases [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48].…”

NECI: N-Electron Configuration Interaction with emphasis on state-of-the-art stochastic methods

“…Specifically, these walkers 0.25 0.50 0.75 1.00 1. 25 may sample up to double excitations from the currently-occupied determinants (a similar argument can be used to justify the above adaptive shift approach). In analogy with a comparable approach taken in selected CI methods, these discarded walkers can be used to sample a second-order correction to the energy from Epstein-Nesbet perturbation theory.…”

“…More recently, a fully spin-adapted formulation of FCIQMC has been implemented based on the Graphical Unitary Group Approach 8 , which overcomes the previous limitations of spin-adaptation, which severely limited the number of open-shell orbitals which could be handled. Other advanced developments of FCIQMC in the NECI code include real-time propagation and application to spectroscopy 21 , Krylovspace FCIQMC 12 , and the similarity transformed FCIQMC [22][23][24][25] which allows the direct incorporation of Jastrow and similar factors depending on explicit electron-electron variables into the wavefunction.…”

Vortices in rotating Bose gas interacting via finite range Gaussian potential in a quasi-two-dimensional harmonic trap

“…( 3) is prefferable wich can be expanded within the finite number of single particle basis states. [28,29].…”