Convergence properties of the effective theory for trapped bosons

Tölle, S.; Hammer, H. W.; Metsch, B.

doi:10.1088/0954-3899/40/5/055004

Cited by 10 publications

(19 citation statements)

References 64 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this Section, we construct a chiral interaction at NLO from realistic phase shifts, and subsequently utilize it in coupled-cluster calculations of 4 He, 16 O, 40 Ca, 90 Zr, and 132 Sn. Our main objectives are (i) to present a proof-of-principle optimization of a realistic interaction within the framework of the oscillator EFT, and (ii) to demonstrate that such an interaction converges fast even in heavy nuclei.…”

Section: Nlo Interactions In Oscillator Eft and Many-body Resultsmentioning

confidence: 99%

“…The LECs, also shown in Table III, are natural in size and similar to NLO sim ; the largest deviation is for the LEC C1 P1 which is only about 1 /3 of its NLO sim counterpart. We utilize the NLO interaction in coupled-cluster calculations at the singles and doubles level (CCSD) [21,66,67] of the nuclei 4 He, 16 O, 40 Ca, 90 Zr, and 132 Sn. The coupled-cluster calculations use Hartree-Fock bases that are unitarily equivalent to the oscillator bases but lead to improved results.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Effective field theory in the harmonic oscillator basis

et al. 2016

View full text Add to dashboard Cite

We develop interactions from chiral effective field theory (EFT) that are tailored to the harmonic oscillator basis. As a consequence, ultraviolet convergence with respect to the model space is implemented by construction and infrared convergence can be achieved by enlarging the model space for the kinetic energy. In oscillator EFT, matrix elements of EFTs formulated for continuous momenta are evaluated at the discrete momenta that stem from the diagonalization of the kinetic energy in the finite oscillator space. By fitting to realistic phase shifts and deuteron data we construct an effective interaction from chiral EFT at next-to-leading order. Many-body coupledcluster calculations of nuclei up to 132 Sn converge fast for the ground-state energies and radii in feasible model spaces.

show abstract

Section: Nlo Interactions In Oscillator Eft and Many-body Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

Effective field theory in the harmonic oscillator basis

et al. 2016

View full text Add to dashboard Cite

show abstract

“…The second error is due to the truncation of the three-body term in equation (20). To estimate this error, we note that according to (26)…”

Section: Resultsmentioning

confidence: 99%

“…where A is some constant that depends on g. Note that this convergence is faster than in a harmonic oscillator [26,27] where it is described by n 1…”

Section: Appendix C Convergence Of the Two Body Energymentioning

confidence: 95%

Flow equations for cold Bose gases

Volosniev

Hammer

2017

New J. Phys.

Self Cite

View full text Add to dashboard Cite

We derive flow equations for cold atomic gases with one macroscopically populated energy level. The generator is chosen such that the ground state decouples from all other states in the system as the renormalization group flow progresses. We propose a self-consistent truncation scheme for the flow equations at the level of three-body operators and show how they can be used to calculate the ground state energy of a general N-body system. Moreover, we provide a general method to estimate the truncation error in the calculated energies. Finally, we test our scheme by benchmarking to the exactly solvable Lieb-Liniger model and find good agreement for weak and moderate interaction strengths.

show abstract

“…While we believe that our four-boson spectrum has the same key characteristics-such as the energy level crossings and spacings as well as the classification into universal and non-universal states-as the ones one would obtain for the zero-range model III, we did not attempt to extrapolate our results to the r 0 → 0 and R 0 → 0 limits. References [49,50] pursued this, finding the values of −0.1(2)E ho , 2.7(3)E ho , and 4.6(5)E ho for the lowest three relative four-boson energies, for the lowest relative twoand three-boson energies both fixed at E ho /2. Our three lowest four-boson energies (see Table II; due to our finite value of r 0 , our two-boson energy is 0.5103E ho and not E ho /2) lie within the estimated numerical errorbars of Ref.…”

Section: N = 4 Systemmentioning

confidence: 92%

Harmonically trapped four-boson system

2018

View full text Add to dashboard Cite

Four identical spinless bosons with purely attractive two-body short-range interactions and repulsive three-body interactions under external spherically symmetric harmonic confinement are considered. The repulsive three-body potential prevents the formation of deeply-bound states with molecular character. The low-energy spectrum with vanishing orbital angular momentum and positive parity for infinitely large two-body s-wave scattering length is analyzed in detail. Using the three-body contact, states are classified as universal, quasi-universal, or strongly non-universal. Connections with the zero-range interaction model are discussed. The energy spectrum is mapped out as a function of the two-body s-wave scattering length as, as > 0. In the weakly-to medium-stronglyinteracting regime, one of the states approaches the energy obtained for a hard core interaction model. This state is identified as the energetically lowest-lying "BEC state". Structural properties are also presented.PACS numbers:

show abstract

Convergence properties of the effective theory for trapped bosons

Cited by 10 publications

References 64 publications

Effective field theory in the harmonic oscillator basis

Effective field theory in the harmonic oscillator basis

Flow equations for cold Bose gases

Harmonically trapped four-boson system

Contact Info

Product

Resources

About