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Register a new userToward Scalable Many-Body Calculations for Nuclear Open Quantum Systems using the Gamow Shell Model
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Drip-line nuclei have very different properties from those of the valley of stability, as they are weakly bound and resonant. Therefore, the models devised for stable nuclei can no longer be applied therein. Hence, a new theoretical tool, the Gamow Shell Model (GSM), has been developed to study the many-body states occurring at the limits of the nuclear chart. GSM is a configuration interaction model based on the use of the so-called Berggren basis, which contains bound, resonant and scattering states, so that inter-nucleon correlations are fully taken into account and the asymptotes of extended many-body wave functions are precisely handled. However, large complex symmetric matrices must be diagonalized in this framework, therefore the use of very powerful parallel machines is needed therein. In order to fully take advantage of their power, a 2D partitioning scheme using hybrid MPI/OpenMP parallelization has been developed in our GSM code. The specificities of the 2D partitioning scheme in the GSM framework will be described and illustrated with numerical examples. It will then be shown that the introduction of this scheme in the GSM code greatly enhances its capabilities.
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Coupling a quantum many-body system to an external environment dramatically changes its dynamics and offers novel possibilities not found in closed systems. Of special interest are the properties of the steady state of such open quantum many-body systems, as well as the relaxation dynamics towards the steady state. However, new computational tools are required to simulate open quantum many-body systems, as methods developed for closed systems cannot be readily applied. We review several approaches to simulate open many-body systems and point out the advances made in recent years towards the simulation of large system sizes.
It is often computationally advantageous to model space as a discrete set of points forming a lattice grid. This technique is particularly useful for computationally difficult problems such as quantum many-body systems. For reasons of simplicity and familiarity, nearly all quantum many-body calculations have been performed on simple cubic lattices. Since the removal of lattice artifacts is often an important concern, it would be useful to perform calculations using more than one lattice geometry. In this work we show how to perform quantum many-body calculations using auxiliary-field Monte Carlo simulations on a three-dimensional body-centered cubic (BCC) lattice. As a benchmark test we compute the ground state energy of 33 spin-up and 33 spin-down fermions in the unitary limit, which is an idealized limit where the interaction range is zero and scattering length is infinite. As a fraction of the free Fermi gas energy $E_{rm FG}$, we find that the ground state energy is $E_0/E_{rm FG}= 0.369(2), 0.371(2),$ using two different definitions of the finite-system energy ratio. This is in excellent agreement with recent results obtained on a cubic lattice cite{He:2019ipt}. We find that the computational effort and performance on a BCC lattice is approximately the same as that for a cubic lattice with the same number of lattice points. We discuss how the lattice simulations with different geometries can be used to constrain the size lattice artifacts in simulations of continuum quantum many-body systems.
The existence of multi-neutron systems has always been a debatable question. Indeed, both inter-nucleon correlations and a large continuum coupling occur in these states. We then employ the ab-initio no-core Gamow shell model to calculate the resonant energies and widths of the trineutron and tetraneutron systems with realistic interactions. Our results indicate that trineutron and tetraneutron are both unbound and bear broad widths. The calculated energy and width of tetraneutron are also comparable with recent experimental data. Moreover, our calculations suggest that the energy of trineutron is lower than that of tetraneutron, while its resonance width is also narrower. This strongly suggests that trineutron is more likely to be experimentally observed than tetraneutron. We thus suggest experimentalists to search for trineutron at low energy.
We introduce an exact numerical technique to solve the nuclear pairing Hamiltonian and to determine properties such as the even-odd mass differences or spectral functions for any element within the periodic table for any number of nuclear shells. In particular, we show that the nucleus is a system with small entanglement and can thus be described efficiently using a one-dimensional tensor network (matrix-product state) despite the presence of long-range interactions. Our approach is numerically cheap and accurate to essentially machine precision, even for large nuclei. We apply this framework to compute the even-odd mass differences of all known lead isotopes from $^{178}$Pb to $^{220}$Pb in the very large configuration space of 13 shells between the neutron magic numbers 82 and 184 (i.e., two major shells) and find good agreement with the experiment. To go beyond the ground state, we calculate the two-neutron removal spectral function of $^{210}$Pb which relates to a two-neutron pickup experiment that probes neutron-pair excitations across the gap of $^{208}$Pb. Finally, we discuss the capabilities of our method to treat pairing with non-zero angular momentum. This is numerically more demanding, but one can still determine the lowest excited states in the full configuration space of one major shell with modest effort, which we demonstrate for the $N=126$, $Zgeq 82$ isotones.
Quantum many-body nuclear dynamics is treated at the mean-field level with the time-dependent Hartree-Fock (TDHF) theory. Low-lying and high-lying nuclear vibrations are studied using the linear response theory. The fusion mechanism is also described for light and heavy systems. The latter exhibit fusion hindrance due to quasi-fission. Typical characteristics of quasi-fission, such as contact time and partial symmetrisation of the fragments mass in the exit channel, are reproduced by TDHF calculations. The (multi-)nucleon transfer at sub-barrier energies is also discussed.
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