Are smooth pseudopotentials a good choice for representing short-range interactions?
arXiv:1812.06521 · doi:10.1103/PhysRevA.99.033608
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 -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 re-scaled 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 multi-particle simulations of interacting ultra-cold atom systems are discussed.
arXiv comment11 pages, 2 figures
References in corpus (55)
- Theory of ultracold Fermi gases
- Experimental realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms
- Deterministic Preparation of a Tunable Few-Fermion System
- Observation of Spatial Charge and Spin Correlations in the 2D Fermi-Hubbard Model
- Fermionization of two distinguishable fermions
- Short-Distance Correlation Properties of the Lieb-Liniger System and Momentum Distributions of Trapped One-Dimensional Atomic Gases
- Observation of a pairing pseudogap in a two-dimensional Fermi gas
- Hong-Ou-Mandel atom interferometry in tunnel-coupled optical tweezers
- Few-body physics with ultracold atomic and molecular systems in traps
- General relations for quantum gases in two and three dimensions. Two-component fermions
- Strongly interacting confined quantum systems in one dimension
- Pairing in few-fermion systems with attractive interactions
- BCS-BEC crossover in a two-dimensional Fermi gas
- Two-Dimensional Homogeneous Fermi Gases
- Auxiliary Field quantum Monte Carlo for Strongly Paired Fermions
- Superfluid transition in quasi2D Fermi gases
- Exact Solution of Strongly Interacting Quasi-One-Dimensional Spinor Bose Gases
- Resonantly Interacting Fermions In a Box
- Quantum Hall physics in rotating Bose-Einstein condensates
- Strongly interacting two-dimensional Fermi gases
- Three attractively interacting fermions in a harmonic trap: Exact solution, ferromagnetism, and high-temperature thermodynamics
- Energetics and Structural Properties of Trapped Two-Component Fermi Gases
- Evolution from a Bose-Einstein condensate to a Tonks-Girardeau gas: An exact diagonalization study
- Adiabatic Path to Fractional Quantum Hall States of a Few Bosonic Atoms
- Exact few-body results for strongly correlated quantum gases in two dimensions
- BEC-BCS Crossover of a Trapped Two-Component Fermi Gas with Unequal Masses
- Distinguishability, degeneracy and correlations in three harmonically trapped bosons in one-dimension
- Symmetries of Three Harmonically-Trapped Particles in One Dimension
- Quantum magnetism in strongly interacting one-dimensional spinor Bose systems
- Two trapped particles interacting by a finite-ranged two-body potential in two spatial dimensions
- Many interacting fermions in a one-dimensional harmonic trap: a quantum-chemical treatment
- Sharp crossover from composite fermionization to phase separation in mesoscopic mixtures of ultracold bosons
- Diffusion Monte Carlo study of strongly interacting two-dimensional Fermi gases
- Many-body tunneling dynamics of Bose-Einstein condensates and vortex states in two spatial dimensions
- Effective-interaction approach to the many-boson problem
- Breaking the resilience of a two-dimensional Bose-Einstein condensate to fragmentation
- The -wave scattering length of a Gaussian potential
- Quantum correlations and degeneracy of identical bosons in a 2D harmonic trap
- Accelerating the convergence of exact diagonalization with the transcorrelated method: Quantum gas in one dimension with contact interactions
- Simulating strongly correlated multiparticle systems in a truncated Hilbert space
- Quantum Hall fractions in ultracold fermionic vapors
- Numerically exact approach to few-body problems far from a perturbative regime
- Harmonically trapped two-atom systems: Interplay of short-range s-wave interaction and spin-orbit coupling
- Cold Fermionic Atoms in Two-Dimensional Traps -- Pairing versus Hund's Rule
- Beyond mean-field dynamics of ultra-cold bosonic atoms in higher dimensions: facing the challenges with a multi-configurational approach
- Self-consistent calculation of the coupling constant in the Gross-Pitaevskii equation
- On the renormalization of contact interactions for the configuration-interaction method in two dimensions
- Pseudopotential for the 2D contact interaction
- Abnormal Superfluid Fraction of Harmonically Trapped Few-Fermion Systems
- Ultracold bosonic scattering dynamics off a repulsive barrier: coherence loss at the dimensional crossover
- Exact Diagonalization Study of Bose-Condensed Gas with Finite-Range Gaussian Interaction
- High-fidelity pseudopotentials for the contact interaction
- Harmonically trapped fermions in two dimensions: ground-state energy and contact of SU(2) and SU(4) systems via nonuniform lattice Monte Carlo
- Fermionic properties of two interacting bosons in a two-dimensional harmonic trap
- Pairing in ultracold Fermi gases in the lowest Landau level
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- Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
- Eliminating the wave function singularity for ultracold atoms by similarity transformation
- Pairing in two-dimensional Fermi gases with a coordinate-space potential
- Vortices in the Many-Body Excited States of Interacting Bosons in Two Dimension