Pseudopotential for the two-dimensional contact interaction

Whitehead, Thomas M.; Schonenberg, LM; Kongsuwan, Nuttawut; Needs, R. J.; Conduit, Gareth

doi:10.1103/physreva.93.042702

Cited by 17 publications

(22 citation statements)

References 59 publications

(124 reference statements)

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“…Following Refs. [28][29][30], we propose a UTP that takes a polynomial form within a cutoff radius r c ,…”

Section: B Utpmentioning

confidence: 99%

“…In particular, the cutoff radius should be chosen less than the interparticle spacing so that three-body scattering events are rare; we therefore follow the approach by Refs. [28][29][30] and set r c = 1/k F to balance statistical and systematic errors in the QMC results.…”

Section: B Utpmentioning

confidence: 99%

“…This is complemented by variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) simulations in the strongly interacting regime, for which we develop an ultratransferable pseudopotential (UTP) following Refs. [27][28][29][30] that is calibrated to deliver both the correct scattering phase shift and correct binding energy for the two-body bound state for −1.5 ≤ k 2 F R 2 eff ≤ 0. Exploiting the UTP, we first revisit the case R 2 eff = 0 [21][22][23], which we next use as a concrete basis to analyze R 2 eff < 0 by considering the ground-state energy, condensate fraction, momentum distribution, and paircorrelation functions.…”

Section: Introductionmentioning

confidence: 99%

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Effective-range dependence of two-dimensional Fermi gases

2017

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The Feshbach resonance provides precise control over the scattering length and effective range of interactions between ultracold atoms. We propose the ultratransferable pseudopotential to model effective interaction ranges −1.5 ≤ k 2 F R 2 eff ≤ 0, where R eff is the effective range and kF is the Fermi wave vector, describing narrow to broad Feshbach resonances. We develop a mean-field treatment and exploit the pseudopotential to perform a variational and diffusion Monte Carlo study of the ground state of the two-dimensional Fermi gas, reporting on the ground-state energy, contact, condensate fraction, momentum distribution, and pair-correlation functions as a function of the effective interaction range across the BEC-BCS crossover. The limit k 2 F R 2 eff → −∞ is a gas of bosons with zero binding energy, whereas ln(kFa) → −∞ corresponds to noninteracting bosons with infinite binding energy.

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“…Following Refs. [28][29][30], we propose a UTP that takes a polynomial form within a cutoff radius r c ,…”

Section: B Utpmentioning

confidence: 99%

Section: B Utpmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Effective-range dependence of two-dimensional Fermi gases

2017

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“…In contrast, the mechanism described by Girardeau whereby the particles can avoid feeling the interaction remains a possibility. In our previous work [20], considering two, three, and four particles [21] in a two dimensional harmonic trap [2,[22][23][24][25][26][27][28][29][30], we showed that interacting bosons avoid feeling the interaction by becoming correlated in such a way that the probability of two particles being at the same position vanishes [31].…”

Section: Introductionmentioning

confidence: 99%

Fermionic Properties of Two Interacting Bosons in a Two-Dimensional Harmonic Trap

2018

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Abstract:The system of two interacting bosons in a two-dimensional harmonic trap is compared with the system consisting of two noninteracting fermions in the same potential. In particular, we discuss how the properties of the ground state of the system, e.g., the different contributions to the total energy, change as we vary both the strength and range of the atom-atom interaction. In particular, we focus on the short-range and strong interacting limit of the two-boson system and compare it to the noninteracting two-fermion system by properly symmetrizing the corresponding degenerate ground state wave functions. In that limit, we show that the density profile of the two-boson system has a tendency similar to the system of two noninteracting fermions. Similarly, the correlations induced when the interaction strength is increased result in a similar pair correlation function for both systems.

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“…Specifically we consider what the requirements are for the basis set to reach the regime of exponential convergence and whether this approach is feasible for multiparticle simulations. Examples of finite-range pseudopotentials used in the literature are the Troullier-Martins [43,44], Pöschl-Teller [45,46], and Gaussian potentials [26,36,[47][48][49][50][51][52][53][54][55][56][57], in addition to the square well popular in diffusion Monte Carlo simulations [48].…”

Section: Introductionmentioning

confidence: 99%

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

2019

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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.

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Pseudopotential for the two-dimensional contact interaction

Cited by 17 publications

References 59 publications

Effective-range dependence of two-dimensional Fermi gases

Effective-range dependence of two-dimensional Fermi gases

Fermionic Properties of Two Interacting Bosons in a Two-Dimensional Harmonic Trap

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

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