Particle-hole excitations in the interacting boson model

Jean-Paul Blaizot, Eugene R. Marshalek

Kapil M. Khanna, B.K. Das

V. Baran, Doru Sabin Delion

We study the description of single-species and isovector pairing correlations in the framework of the projected-BCS (PBCS) and the quartet condensation model (QCM) from a particle-hole perspective, and we introduce the representation of the QCM quartet condensate state in terms of particle-hole excitations with respect to the Hartree-Fock state. We also present a new bosonic approximation for both PBCS and QCM. In each case, the starting point is the reformulation of the pair and quartet condensate states in terms of particle-hole excitations with respect to the Hartree-Fock state. The main simplification of our approach is the assumption that the pair operators corresponding to both particle and hole states obey bosonic commutation relations. This simplifies tremendously the computations and allows for an analytic derivation of the averaged Hamiltonian on the condensate state as a function of the mixing amplitudes. We study both the pure bosonic approach and the renormalized version and compare the particle-hole bosonic version to the naive prescription of applying the boson approximation directly to the original condensate state. We compare the fermionic and the renormalized particle-hole bosonic approaches in the case of a picket-fence model of doubly degenerate states and in a realistic shell-model space with an effective interaction for the $N=Z$ nuclei above $^{100}\mathrm{Sn}$.

Robert Seiringer

M. Tomaselli, L C Liu, T K hl +3 more

The structure and dynamics of an n -particle system are described with coupled nonlinear Heisenberg commutator equations where the nonlinear terms are generated by the two-body interaction that excites the reference vacuum via particle–particle and particle–hole excitations. Nonperturbative solutions of the system are obtained with the use of the dynamic linearization approximation and cluster transformation coefficients. The dynamic linearization approximation converts the commutator chain into an eigenvalue problem. The cluster coefficients factorize the matrix elements of the ( n ) particles or particle–hole systems in terms of the matrix elements of the ( n − 1)-systems coupled to particle–particle, particle–hole and hole–hole bosons. Group properties of the particle–particle, particle–hole and hole–hole permutation groups simplify the calculation of these coefficients. The particle–particle vacuum excitations generate superconductive diagrams in the dynamics of three-quark systems. Applications of the model to fermionic and bosonic systems are discussed.

N. G. Zhang, Christopher L. Henley

We consider a Hubbard-like model of strongly interacting spinless fermions and hardcore bosons on a square lattice, such that nearest neighbor occupation is forbidden. Stripes (lines of holes across the lattice forming antiphase walls between ordered domains) are a favorable way to dope this system below half filling. The problem of a single stripe can be mapped to fermions in one dimension, which allows understanding of its elementary excitations and calculation of the stripe's effective mass for transverse vibrations. Using Lanczos exact diagonalization, we investigate the excitation gap and dispersion of a hole on a stripe, and the interaction of two holes. We also study the interaction of a few stripes, finding that they repel and the interaction energy decays with stripe separation as if they are hardcore particles moving in one (transverse) direction. To determine the stability of an array of stripes against phase separation into a particle-rich phase and a hole-rich liquid, we evaluate the liquid's equation of state, finding that the stripe-array is not stable for bosons but is possibly stable for fermions.