532 research outputs found
The Density Matrix Renormalization Group Method and Large-Scale Nuclear Shell-Model Calculations
The particle-hole Density Matrix Renormalization Group (p-h DMRG) method is
discussed as a possible new approach to large-scale nuclear shell-model
calculations. Following a general description of the method, we apply it to a
class of problems involving many identical nucleons constrained to move in a
single large j-shell and to interact via a pairing plus quadrupole interaction.
A single-particle term that splits the shell into degenerate doublets is
included so as to accommodate the physics of a Fermi surface in the problem. We
apply the p-h DMRG method to this test problem for two values, one for
which the shell model can be solved exactly and one for which the size of the
hamiltonian is much too large for exact treatment. In the former case, the
method is able to reproduce the exact results for the ground state energy, the
energies of low-lying excited states, and other observables with extreme
precision. In the latter case, the results exhibit rapid exponential
convergence, suggesting the great promise of this new methodology even for more
realistic nuclear systems. We also compare the results of the test calculation
with those from Hartree-Fock-Bogolyubov approximation and address several other
questions about the p-h DMRG method of relevance to its usefulness when
treating more realistic nuclear systems
Fully Self-consistent RPA description of the many level pairing model
The Self-Consistent RPA (SCRPA) equations in the particle-particle channel
are solved without any approximation for the picket fence model. The results
are in excellent agreement with the exact solutions found with the Richardson
method. Particularly interesting features are that screening corrections
reverse the sign of the interaction and that SCRPA yields the exact energies in
the case of two levels with two particles.Comment: 37 pages, 1 figure and 17 table
Pairing in 4-component fermion systems: the bulk limit of SU(4)-symmetric Hamiltonians
Fermion systems with more than two components can exhibit pairing condensates
of much more complex structure than the well-known single BCS condensate of
spin-up and spin-down fermions. In the framework of the exactly solvable SO(8)
Richardson-Gaudin model with SU(4)-symmetric Hamiltonians, we show that the BCS
approximation remains valid in the thermodynamic limit of large systems for
describing the ground state energy and the canonical and quasiparticle
excitation gaps. Correlations beyond BCS pairing give rise to a spectrum of
collective excitations, but these do not affect the bulk energy and
quasiparticle gaps.Comment: 13 pages; 2 figures; 1 tabl
Pair Fluctuations in Ultra-small Fermi Systems within Self-Consistent RPA at Finite Temperature
A self-consistent version of the Thermal Random Phase Approximation (TSCRPA)
is developed within the Matsubara Green's Function (GF) formalism. The TSCRPA
is applied to the many level pairing model. The normal phase of the system is
considered. The TSCRPA results are compared with the exact ones calculated for
the Grand Canonical Ensemble. Advantages of the TSCRPA over the Thermal Mean
Field Approximation (TMFA) and the standard Thermal Random Phase Approximation
(TRPA) are demonstrated. Results for correlation functions, excitation
energies, single particle level densities, etc., as a function of temperature
are presented.Comment: 22 pages, 13 figers and 3 table
Valence Bond Mapping of Antiferromagnetic Spin Chains
Boson mapping techniques are developed to describe valence bond correlations
in quantum spin chains. Applying the method to the alternating bond hamiltonian
for a generic spin chain, we derive an analytic expression for the transition
points which gives perfect agreement with existing Density Matrix
Renormalization Group (DMRG) and Quantum Monte Carlo (QMC) calculations.Comment: 10 pages, Revte
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