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arXiv:1612.08004 · Physical Review Letters

Effective Forces Between Quantum Bound States

Alexander Rokash, E. Epelbaum, HERMANN KREBS, Dean Lee

Published Jun 9, 2017• 9 citations
arXivHTMLPDF

Abstract

Recent ab initio lattice studies have found that the interactions between alpha particles (^{4}He nuclei) are sensitive to seemingly minor details of the nucleon-nucleon force, such as interaction locality. In order to uncover the essential physics of this puzzling phenomenon without unnecessary complications, we study a simple model involving two-component fermions in one spatial dimension. We probe the interaction between two bound dimers for several different particle-particle interactions and measure an effective potential between the dimers using external point potentials which act as numerical tweezers. We find that the strength and range of the local part of the particle-particle interactions play a dominant role in shaping the interactions between the dimers and can even determine the overall sign of the effective potential.

DOI
10.1103/physrevlett.118.232502

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Recent ab initio lattice studies have found that the interactions between alpha particles (^{4}He nuclei) are sensitive to seemingly minor details of the nucleon-nucleon force, such as interaction locality. In order to uncover the essential physics of this puzzling phenomenon without unnecessary complications, we study a simple model involving two-component fermions in one spatial dimension. We probe the interaction between two bound dimers for several different particle-particle interactions and measure an effective potential between the dimers using external point potentials which act as numerical tweezers. We find that the strength and range of the local part of the particle-particle interactions play a dominant role in shaping the interactions between the dimers and can even determine the overall sign of the effective potential.
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Abstract Ab initio calculations have an essential role in our fundamental understanding of quantum many-body systems across many subfields, from strongly correlated fermions 1–3 to quantum chemistry 4–6 and from atomic and molecular systems 7–9 to nuclear physics 10–14 . One of the primary challenges is to perform accurate calculations for systems where the interactions may be complicated and difficult for the chosen computational method to handle. Here we address the problem by introducing an approach called wavefunction matching. Wavefunction matching transforms the interaction between particles so that the wavefunctions up to some finite range match that of an easily computable interaction. This allows for calculations of systems that would otherwise be impossible owing to problems such as Monte Carlo sign cancellations. We apply the method to lattice Monte Carlo simulations 15,16 of light nuclei, medium-mass nuclei, neutron matter and nuclear matter. We use high-fidelity chiral effective field theory interactions 17,18 and find good agreement with empirical data. These results are accompanied by insights on the nuclear interactions that may help to resolve long-standing challenges in accurately reproducing nuclear binding energies, charge radii and nuclear-matter saturation in ab initio calculations 19,20 .
We present a diagrammatic approach for the dimer-dimer scattering problem in two or three spatial dimensions, within the resonance approximation where these dimers are in a weakly bound resonant state. This approach is first applied to the calculation of the dimer-dimer scattering length aB{a}_{B}aB​ in three spatial dimensions, for dimers made of two fermions in a spin-singlet state, with corresponding scattering length aF{a}_{F}aF​, and the already known result aB=0.60{a}_{B}=0.60aB​=0.60 aF{a}_{F}aF​ is recovered exactly. Then we make use of our approach to obtain results in two spatial dimensions for fermions as well as for bosons. Specifically, we calculate bound-state energies for three bbbbbbbbb and four bbbbbbbbbbbb resonantly interacting bosons in two dimensions. We consider also the case of a resonant interaction between fermions and bosons, and we obtain the exact bound-state energies of two bosons plus one fermion bbfbbfbbf, two bosons plus two fermions $b{f}_{\ensuremath{\uparrow}}b{f}_{\ensuremath{\downarrow}}$, and three bosons plus one fermion bbbfbbbfbbbf.
Ab initio nuclear physics tackles the problem of strongly interacting four-component fermions. The same setting could foreseeably be probed experimentally in ultracold atomic systems, where two- and three-component experiments have led to major breakthroughs in recent years. Both due to the problem's inherent interest and as a pathway to nuclear physics, in this Letter we study four-component fermions at unitarity via the use of quantum Monte Carlo methods. We explore novel forms of the trial wave function and find one which leads to a ground state of the eight-particle system whose energy is almost equal to that of two four-particle systems. We investigate the clustering properties involved and also extrapolate to the zero-range limit. In addition to being experimentally testable, our results impact the prospects of developing nuclear physics as a perturbation around the unitary limit.
Strongly-interacting ultra-cold atoms in tight-binding optical lattice potentials provide an ideal platform to realize the fundamental Hubbard model. Here, after outlining the elementary single particle solution, we review and expand our recent work on complete characterization of the bound and scattering states of two and three bosonic atoms in a one-dimensional optical lattice. In the case of two atoms, there is a family of interaction-bound "dimer" states of co-localized particles that exists invariantly for either attractive or repulsive on-site interaction, with the energy below or above the two-particle scattering continuum, respectively. Adding then the third particle -- "monomer" -- we find that, apart from the simple strongly-bound "trimer" corresponding to all three particles occupying the same lattice site, there are two peculiar families of weakly-bound trimers with energies below and above the monomer-dimer scattering continuum, the corresponding binding mechanism being an effective particle exchange interaction.