Volume dependence of N-body bound states

König, S.; Lee, Dean

doi:10.1016/j.physletb.2018.01.060

Cited by 64 publications

(70 citation statements)

References 78 publications

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“…The second bound state is predominately a bound state of a particle and a tightly bound dimer, so its L dependence is governed by the two-body Lüscher formula [46]; see also Refs. [3,47]. The shift is again negative:…”

Section: Bound Statesmentioning

confidence: 95%

Three-body spectrum in a finite volume: The role of cubic symmetry

et al. 2018

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The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the BetheSalpeter equation for particle-dimer scattering is expanded in the basis functions of different irreducible representations of the octahedral group. Such a projection is of particular importance for the three-body problem in the finite volume due to the occurrence of three-body singularities above breakup. Additionally, we study the numerical solution and properties of such a projected quantization condition in a simple model. It is shown that, for large volumes, these solutions allow for an instructive interpretation of the energy eigenvalues in terms of bound and scattering states.

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Section: Bound Statesmentioning

confidence: 95%

Three-body spectrum in a finite volume: The role of cubic symmetry

et al. 2018

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“…For finite-volume corrections to the binding energy of N -particle quantum bound states on the lattice we refer the reader to Ref. [29]. The leading-order (LO) IR extrapolation formula for energies is…”

Section: Introductionmentioning

confidence: 99%

Large-scale exact diagonalizations reveal low-momentum scales of nuclei

et al. 2018

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Ab initio methods aim to solve the nuclear many-body problem with controlled approximations. Virtually exact numerical solutions for realistic interactions can only be obtained for certain special cases such as few-nucleon systems. Here we extend the reach of exact diagonalization methods to handle model spaces with dimension exceeding 10 10 on a single compute node. This allows us to perform no-core shell model (NCSM) calculations for 6 Li in model spaces up to Nmax = 22 and to reveal the 4 He+d halo structure of this nucleus. Still, the use of a finite harmonic-oscillator basis implies truncations in both infrared (IR) and ultraviolet (UV) length scales. These truncations impose finite-size corrections on observables computed in this basis. We perform IR extrapolations of energies and radii computed in the NCSM and with the coupled-cluster method at several fixed UV cutoffs. It is shown that this strategy enables information gain also from data that is not fully UV converged. IR extrapolations improve the accuracy of relevant bound-state observables for a range of UV cutoffs, thus making them profitable tools. We relate the momentum scale that governs the exponential IR convergence to the threshold energy for the first open decay channel. Using large-scale NCSM calculations we numerically verify this small-momentum scale of finite nuclei.

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“…Such a QC in fact exists in the literature [48,49,50,51,52,53,54,55,56], although often in radically different forms, and its implementation appears more complex than the two-body QC [57,58,59]. An ongoing effort in the community is devoted to exploring the consistency of these forms and their various limits [60,61,62,63], either formally, or through comparing their output for the FV spectra. Here, we briefly describe one of these approaches and refer the reader to other proceedings in this conference series for more recent work [64,65].…”

Section: Three-body Elastic Scatteringmentioning

confidence: 99%

The path from finite to infinite volume: Hadronic observables from lattice QCD

Davoudi¹

2019

Proceedings of the 36th Annual International Symposium on Lattice Field Theory — PoS(LATTICE2018)

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Standard Model determinations of properties of strongly interacting systems of hadrons have become possible with the powerful method of lattice quantum chromodynamics (LQCD), a method with growing applicability and reliability. While growth in computational power and innovations in algorithmic and computational approaches have been essential in advancing the state of the field, conceptual and formal developments have played a crucial role in turning the output of LQCD computations to phenomenologically valuable results. From the invention of finitevolume technology to access physical observables by Martin Lüscher over three decades ago to date, this field has grown in scope and complexity, enabling studies of scattering amplitudes and reaction rates, as well as spectroscopy of excited states of quantum chromodynamics (QCD) and resonances. Further, LQCD studies are augmented with the inclusion of quantum electrodynamics (QED), and subtleties related to the finite volume of systems in presence of QED have been understood and largely controlled. In this talk, I focus on selected developments to give a taste of the status of the field concerning the mapping between the finite and infinite-volume physics and its state-of-the-art applications.

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Volume dependence of N-body bound states

Cited by 64 publications

References 78 publications

Three-body spectrum in a finite volume: The role of cubic symmetry

Three-body spectrum in a finite volume: The role of cubic symmetry

Large-scale exact diagonalizations reveal low-momentum scales of nuclei

The path from finite to infinite volume: Hadronic observables from lattice QCD

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