80 research outputs found
Stochastic extension of the Lanczos method for nuclear shell-model calculations with variational Monte Carlo method
We propose a new variational Monte Carlo (VMC) approach based on the Krylov
subspace for large-scale shell-model calculations. A random walker in the VMC
is formulated with the -scheme representation, and samples a small number of
configurations from a whole Hilbert space stochastically. This VMC framework is
demonstrated in the shell-model calculations of Cr and Zn, and we
discuss its relation to a small number of Lanczos iterations. By utilizing the
wave function obtained by the conventional particle-hole-excitation truncation
as an initial state, this VMC approach provides us with a sequence of
systematically improved results.Comment: 5 pages, 4 figures, submitted to Physics Letters
Gaplessness of the Gaffnian
We study the Gaffnian trial wavefunction proposed to describe fractional
quantum Hall correlations at Bose filling factor and Fermi filling
. A family of Hamiltonians interpolating between a hard-core
interaction for which the physics is known and a projector whose ground state
is the Gaffnian is studied in detail. We give evidence for the absence of a gap
by using large-scale exact diagonalizations in the spherical geometry. This is
in agreement with recent arguments based on the fact that this wavefunction is
constructed from a non-unitary conformal field theory. By using the cylinder
geometry, we discuss in detail the nature of the underlying minimal model and
we show the appearance of heterotic conformal towers in the edge energy
spectrum where left and right movers are generated by distinct primary
operators.Comment: 11 pages, 5 figure
Extrapolation method in shell model calculations with deformed basis
An extrapolation method in shell model calculations with deformed basis is
presented, which uses a scaling property of energy and energy variance for a
series of systematically approximated wave functions to the true one. Such
approximated wave functions are given by variation-after-projection method
concerning the full angular momentum projection. This extrapolation needs
energy variance, which amounts to the calculation of expectation value of
square of Hamiltonian . We present the method to evaluate this
matrix element and show that large reduction of its numerical computation can
be done by taking an advantage of time-reversal symmetry. The numerical tests
are presented for shell calculations with a realistic residual
interaction.Comment: 5 pages, 2 figures, accepted for publication in Phys. Rev.
Anomalous Properties of Quadrupole Collective States in Te and beyond
The ground and low-lying states of neutron-rich exotic Te and Sn isotopes are
studied in terms of the nuclear shell model by the same Hamiltonian used for
the spherical-deformed shape phase transition of Ba isotopes, without any
adjustment. An anomalously small value is obtained for
in Te, consistently with a recent experiment. The levels of Te
up to yrast are shown to be in agreement with observed ones. It is
pointed out that Te can be an exceptionally suitable case for studying
mixed-symmetry 1, 2 and 3 states, and predictions are made for
energies, M1 and E2 properties. Systematic trends of structure of heavier and
more exotic Sn and Te isotopes beyond Te are studied by Monte Carlo
Shell Model, presenting an unusual and very slow evolution of
collectivity/deformation.Comment: 8 pages, 7 figures, accepted for publication in Phys. Rev.
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