Generalized isotropic Lipkin-Meshkov-Glick models: ground state entanglement and quantum entropies

We introduce a new class of generalized isotropic Lipkin–Meshkov–Glick models with su(m+1) spin and long-range non-constant interactions, whose non-degenerate ground state is a Dicke state of su(m+1) type. We evaluate in closed form the reduced density matrix of a block of Lspins when the whole system is in its ground state, and study the corresponding von Neumann and Rényi entanglement entropies in the thermodynamic limit. We show that both of these entropies scale as a log L when L tends to infinity, where the coefficient a is equal to (m  −  k)/2 in the ground state phase with k vanishing magnon densities. In particular, our results show that none of these generalized Lipkin–Meshkov–Glick models are critical, since when L-->∞ their Rényi entropy R_q becomes independent of the parameter q. We have also computed the Tsallis entanglement entropy of the ground state of these generalized su(m+1) Lipkin–Meshkov–Glick models, finding that it can be made extensive by an appropriate choice of its parameter only when m-k≥3. Finally, in the su(3) case we construct in detail the phase diagram of the ground state in parameter space, showing that it is determined in a simple way by the weights of the fundamental representation of su(3). This is also true in the su(m+1) case; for instance, we prove that the region for which all the magnon densities are non-vanishing is an (m  +  1)-simplex in R^m whose vertices are the weights of the fundamental representation of su(m+1).

Direct experimental evidence for a multiparticle-hole ground state configuration of deformed Mg-33

The first direct experimental evidence of a multiparticle-hole ground state configuration of the neutron-rich Mg-33 isotope has been obtained via intermediate energy (400 A MeV) Coulomb dissociation measurement. The major part similar to(70 +/- 13)% of the cross section is observed to populate the excited states of Mg-32 after the Coulomb breakup of Mg-33. The shapes of the differential Coulomb dissociation cross sections in coincidence with different core excited states favor that the valence neutron occupies both the s(1/2) and p(3/2) orbitals. These experimental findings suggest a significant reduction and merging of sd-pf shell gaps at N similar to 20 and 28. The ground state configuration of Mg-33 is predominantly a combination of Mg-32(3.0,3.5MeV; 2(-), 1(-)) circle times nu(s1/2), Mg-32(2.5MeV; 2(+)) circle times nu(p3/2), and Mg-32(0; 0(+)) circle times nu(p3/2). The experimentally obtained quantitative spectroscopic information for the valence neutron occupation of the s and p orbitals, coupled with different core states, is in agreement with Monte Carlo shell model (MCSM) calculation using 3 MeV as the shell gap at N = 20.