1,594 research outputs found
Quantum Probabilistic Subroutines and Problems in Number Theory
We present a quantum version of the classical probabilistic algorithms
la Rabin. The quantum algorithm is based on the essential use of
Grover's operator for the quantum search of a database and of Shor's Fourier
transform for extracting the periodicity of a function, and their combined use
in the counting algorithm originally introduced by Brassard et al. One of the
main features of our quantum probabilistic algorithm is its full unitarity and
reversibility, which would make its use possible as part of larger and more
complicated networks in quantum computers. As an example of this we describe
polynomial time algorithms for studying some important problems in number
theory, such as the test of the primality of an integer, the so called 'prime
number theorem' and Hardy and Littlewood's conjecture about the asymptotic
number of representations of an even integer as a sum of two primes.Comment: 9 pages, RevTex, revised version, accepted for publication on PRA:
improvement in use of memory space for quantum primality test algorithm
further clarified and typos in the notation correcte
Dispersion of a single hole in the t-J model
The dispersion of a single hole in the t-J model obtained by the exact result
of 32 sites and the results obtained by self-consistent Born approximation and
the Green function Monte Carlo method can be simply derived by a mean-field
theory with d-RVB and antiferromagnetic order parameters. In addition, it
offers a simple explanation for the difference observed between those results.
The presence of the extended van Hove region at (pi,0) is a consequence of the
d-RVB pairing independenct of the antiferromagnetic order. Results including t'
and t" are also presented and explained consistently in a similar way.Comment: LaTex file, 5 pages with 5 embedded eps figure
Doping dependence of the superconducting gap in Bi2Sr2CaCu2O{8 + delta}
Bi2Sr2CaCu2O{8 + \delta} crystals with varying hole concentrations (0.12 < p
< 0.23) were studied to investigate the effects of doping on the symmetry and
magnitude of the superconducting gap. Electronic Raman scattering experiments
that sample regions of the Fermi surface near the diagonal (B_{2g}) and
principal axes (B_{1g}) of the Brillouin Zone have been utilized. The frequency
dependence of the Raman response function at low energies is found to be linear
for B_{2g} and cubic for B_{1g} (T< T_c). The latter observations have led us
to conclude that the doping dependence of the superconducting gap is consistent
with d_{x^2-y^2} symmetry, for slightly underdoped and overdoped crystals.
Studies of the pair-breaking peak found in the B_{1g} spectra demonstrate that
the magnitude of the maximum gap decreases monotonically with increasing hole
doping, for p > 0.12. Based on the magnitude of the B_{1g} renormalization, it
is found that the number of quasiparticles participating in pairing increases
monotonically with increased doping. On the other hand, the B_{2g} spectra show
a weak "pair-breaking peak" that follows a parabolic-like dependence on hole
concentration, for 0.12 < p < 0.23.Comment: 9 pages REvTex document including 8 eps figures; new table II;
changes to Fig. 5 and tex
The Electron Spectral Function in Two-Dimensional Fractionalized Phases
We study the electron spectral function of various zero-temperature
spin-charge separated phases in two dimensions. In these phases, the electron
is not a fundamental excitation of the system, but rather ``decays'' into a
spin-1/2 chargeless fermion (the spinon) and a spinless charge e boson (the
chargon). Using low-energy effective theories for the spinons (d-wave pairing
plus possible N\'{e}el order), and the chargons (condensed or quantum
disordered bosons), we explore three phases of possible relevance to the
cuprate superconductors: 1) AF*, a fractionalized antiferromagnet where the
spinons are paired into a state with long-ranged N\'{e}el order and the
chargons are 1/2-filled and (Mott) insulating, 2) the nodal liquid, a
fractionalized insulator where the spinons are d-wave paired and the chargons
are uncondensed, and 3) the d-wave superconductor, where the chargons are
condensed and the spinons retain a d-wave gap. Working within the gauge
theory of such fractionalized phases, our results should be valid at scales
below the vison gap. However, on a phenomenological level, our results should
apply to any spin-charge separated system where the excitations have these
low-energy effective forms. Comparison with ARPES data in the undoped,
pseudogapped, and superconducting regions is made.Comment: 10 page
Higgs algebraic symmetry of screened system in a spherical geometry
The orbits and the dynamical symmetries for the screened Coulomb potentials
and isotropic harmonic oscillators have been studied by Wu and Zeng [Z. B. Wu
and J. Y. Zeng, Phys. Rev. A 62,032509 (2000)]. We find the similar properties
in the responding systems in a spherical space, whose dynamical symmetries are
described by Higgs Algebra. There exists a conserved aphelion and perihelion
vector, which, together with angular momentum, constitute the generators of the
geometrical symmetry group at the aphelia and perihelia points .Comment: 8 pages, 1 fi
Anisotropic two-dimensional Heisenberg model by Schwinger-boson Gutzwiller projected method
Two-dimensional Heisenberg model with anisotropic couplings in the and
directions () is considered. The model is first solved in the
Schwinger-boson mean-field approximation. Then the solution is Gutzwiller
projected to satisfy the local constraint that there is only one boson at each
site. The energy and spin-spin correlation of the obtained wavefunction are
calculated for systems with up to sites by means of the
variational Monte Carlo simulation. It is shown that the antiferromagnetic
long-range order remains down to the one-dimensional limit.Comment: 15 pages RevTex3.0, 4 figures, available upon request, GWRVB8-9
Structure and properties of a novel fulleride Sm6C60
A novel fulleride Sm6C60 has been synthesized using high temperature solid
state reaction. The Rietveld refinement on high resolution synchrotron X-ray
powder diffraction data shows that Sm6C60 is isostructural with body-centered
cubic A6C60 (A=K, Ba). Raman spectrum of Sm6C60 is similar to that of Ba6C60,
and the frequencies of two Ag modes in Sm6C60 are nearly the same as that of
Ba6C60, suggesting that Sm is divalent and hybridization between C60 molecules
and the Sm atom could exist in Sm6C60. Resistivity measurement shows a weak
T-linear behavior above 180 K, the transport at low temperature is mainly
dominated by granular-metal theory.Comment: 9 pages, 3 figures, submitted to Phys. Rev. B (March 12, 1999
Hubbard model versus t-J model: The one-particle spectrum
The origin of the apparent discrepancies between the one-particle spectra of
the Hubbard and t-J models is revealed: Wavefunction corrections, in addition
to the three-site terms, should supplement the bare t-J. In this way a
quantitative agreement between the two models is obtained, even for the
intermediate- values appropriate for the high-Tc cuprate superconductors.
Numerical results for clusters of up to 20 sites are presented. The momentum
dependence of the observed intensities in the photoemission spectra of
Sr2CuO2Cl2 are well described by this complete strong-coupling approach.Comment: 4 two-column RevTeX pages, including 4 Postscript figures. Uses epsf.
Accepted for publication in Physical Review B, Rapid Communicatio
Numerical renormalization group study of the 1D t-J model
The one-dimensional (1D) model is investigated using the density matrix
renormalization group (DMRG) method. We report for the first time a
generalization of the DMRG method to the case of arbitrary band filling and
prove a theorem with respect to the reduced density matrix that accelerates the
numerical computation. Lastly, using the extended DMRG method, we present the
ground state electron momentum distribution, spin and charge correlation
functions. The anomaly of the momentum distribution function first
discussed by Ogata and Shiba is shown to disappear as increases. We also
argue that there exists a density-independent beyond which the system
becomes an electron solid.Comment: Wrong set of figures were put in the orginal submissio
The Numerical Renormalization Group Method for correlated electrons
The Numerical Renormalization Group method (NRG) has been developed by Wilson
in the 1970's to investigate the Kondo problem. The NRG allows the
non-perturbative calculation of static and dynamic properties for a variety of
impurity models. In addition, this method has been recently generalized to
lattice models within the Dynamical Mean Field Theory. This paper gives a brief
historical overview of the development of the NRG and discusses its application
to the Hubbard model; in particular the results for the Mott metal-insulator
transition at low temperatures.Comment: 14 pages, 7 eps-figures include
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