Interaction for the trapped fermi gas from a unitary transformation of the exact two-body spectrum

We study systems of few two-component fermions interacting in a Harmonic Oscillator trap. The fermion-fermion interaction is generated in a finite basis with a unitary transformation of the exact two-body spectrum given by the Busch formula. The few-body Schr\"odinger equation is solved with the formalism of the No-Core Shell Model. We present results for a system of three fermions interacting at unitarity as well as for finite values of the S-wave scattering length $a_2$ and effective range $r_2$. Unitary systems with four and five fermions are also considered. We show that the many-body energies obtained in this approach are in excellent agreement with exact solutions for the three-body problem, and results obtained by other methods in the other cases.Comment: 9 pages, 6 figures. Accepted for publication in Eur. Phys. J.

Density matrix renormalization group approach to two-fluid open many-fermion systems

We have extended the density matrix renormalization group (DMRG) approach to two-fluid open many-fermion systems governed by complex-symmetric Hamiltonians. The applications are carried out for three- and four-nucleon (proton-neutron) systems within the Gamow Shell Model (GSM) in the complex-energy plane. We study necessary and sufficient conditions for the GSM+DMRG method to yield the correct ground state eigenvalue and discuss different truncation schemes within DMRG. The proposed approach will enable configuration interaction studies of weakly-bound and unbound strongly interacting complex systems which, because of a prohibitively large size of Fock space, cannot be treated by means of the direct diagonalization.Comment: 13 pages, 15 figure

Density matrix renormalization group approach for many-body open quantum systems

The density matrix renormalization group (DMRG) approach is extended to complex-symmetric density matrices characteristic of many-body open quantum systems. Within the continuum shell model, we investigate the interplay between many-body configuration interaction and coupling to open channels. It is shown that the DMRG technique applied to broad resonances in the unbound neutron-rich nucleus 7He provides a highly accurate treatment of the coupling to the non-resonant scattering continuum.Comment: 4 pages, 3 figure

Effective interactions for light nuclei: an effective (field theory) approach

One of the central open problems in nuclear physics is the construction of effective interactions suitable for many-body calculations. We discuss a recently developed approach to this problem, where one starts with an effective field theory containing only fermion fields and formulated directly in a no-core shell-model space. We present applications to light nuclei and to systems of a few atoms in a harmonic-oscillator trap. Future applications and extensions, as well as challenges, are also considered

Density matrix renormalization group description of the island of inversion isotopes 28−33^{28-33}F

Recent experiments have confirmed that the neutron-rich isotopes $^{28,29}$F belong to the so-called island of inversion (IOI), a region of the nuclear chart around $Z=10$ and $N=20$ where nuclear structure deviates from the standard shell model predictions due to deformation and continuum effects. However, while the general principles leading to the IOI are relatively well understood, the details of the low-lying structure of the exotic fluorine isotopes $^{28-33}$F are basically unknown. In this work, we perform large-scale shell model calculations including continuum states to investigate the properties of the neutron-rich isotopes $^{25-33}$F, using a core of $^{24}$O and an effective two-body interaction with only three adjustable parameters. We adjust the core potential and interaction on experimentally confirmed states in $^{25,26}$O and $^{25-27}$F and solve the many-body problem using the density matrix renormalization group method for open quantum systems in a $sd$-$fp$ model space. We obtain the first detailed spectroscopy of $^{25-33}$F in the continuum and show how the interplay between continuum effects and deformation explains the recent data on $^{28,29}$F, and produces an inversion of the ${5/2}^+$ and ${1/2}^+$ states in $^{29,31,33}$F. Several deformed one- and two-neutron halo states are predicted in $^{29,31}$F, and we predict the ground state of $^{30}$F to have a structure similar to that of the first ${5/2}^+$ state of $^{29}$F. We also suggest several experimental studies to constraint models and test the present predictions. The complex structure of neutron-rich fluorine isotopes offers a trove of information about the formation of the southern shore of the IOI through a subtle interplay of deformation and continuum couplings driven by the occupation of the quasi-degenerate neutron shells $0d_{3/2}$ and $1p_{3/2}$

Fermionization of two-component few-fermion systems in a one-dimensional harmonic trap

The nature of strongly interacting Fermi gases and magnetism is one of the most important and studied topics in condensed-matter physics. Still, there are many open questions. A central issue is under what circumstances strong short-range repulsive interactions are enough to drive magnetic correlations. Recent progress in the field of cold atomic gases allows to address this question in very clean systems where both particle numbers, interactions and dimensionality can be tuned. Here we study fermionic few-body systems in a one dimensional harmonic trap using a new rapidly converging effective-interaction technique, plus a novel analytical approach. This allows us to calculate the properties of a single spin-down atom interacting with a number of spin-up particles, a case of much recent experimental interest. Our findings indicate that, in the strongly interacting limit, spin-up and spin-down particles want to separate in the trap, which we interpret as a microscopic precursor of one-dimensional ferromagnetism in imbalanced systems. Our predictions are directly addressable in current experiments on ultracold atomic few-body systems.Comment: 12 pages, 6 figures, published version including two appendices on our new numerical and analytical approac

Ab-initio No-Core Gamow Shell Model calculations with realistic interactions

No-Core Gamow Shell Model (NCGSM) is applied for the first time to study selected well-bound and unbound states of helium isotopes. This model is formulated on the complex energy plane and, by using a complete Berggren ensemble, treats bound, resonant, and scattering states on equal footing. We use the Density Matrix Renormalization Group method to solve the many-body Schr\"{o}dinger equation. To test the validity of our approach, we benchmarked the NCGSM results against Faddeev and Faddeev-Yakubovsky exact calculations for $^3$H and $^4$He nuclei. We also performed {\textit ab initio} NCGSM calculations for the unstable nucleus $^5$He and determined the ground state energy and decay width, starting from a realistic N$^3$LO chiral interaction.Comment: 17 pages, 14 figures. Revised version. Discussion on microscopic overlap functions, SFs and ANCs is added. Added references. Accepted for publication at PR