672 research outputs found
On SAT representations of XOR constraints
We study the representation of systems S of linear equations over the
two-element field (aka xor- or parity-constraints) via conjunctive normal forms
F (boolean clause-sets). First we consider the problem of finding an
"arc-consistent" representation ("AC"), meaning that unit-clause propagation
will fix all forced assignments for all possible instantiations of the
xor-variables. Our main negative result is that there is no polysize
AC-representation in general. On the positive side we show that finding such an
AC-representation is fixed-parameter tractable (fpt) in the number of
equations. Then we turn to a stronger criterion of representation, namely
propagation completeness ("PC") --- while AC only covers the variables of S,
now all the variables in F (the variables in S plus auxiliary variables) are
considered for PC. We show that the standard translation actually yields a PC
representation for one equation, but fails so for two equations (in fact
arbitrarily badly). We show that with a more intelligent translation we can
also easily compute a translation to PC for two equations. We conjecture that
computing a representation in PC is fpt in the number of equations.Comment: 39 pages; 2nd v. improved handling of acyclic systems, free-standing
proof of the transformation from AC-representations to monotone circuits,
improved wording and literature review; 3rd v. updated literature,
strengthened treatment of monotonisation, improved discussions; 4th v. update
of literature, discussions and formulations, more details and examples;
conference v. to appear LATA 201
Giant infrared intensity of the Peierls mode at the neutral-ionic phase transition
We present exact diagonalization results on a modified Peierls-Hubbard model
for the neutral-ionic phase transition. The ground state potential energy
surface and the infrared intensity of the Peierls mode point to a strong,
non-linear electron-phonon coupling, with effects that are dominated by the
proximity to the electronic instability rather than by electronic correlations.
The huge infrared intensity of the Peierls mode at the ferroelectric
transition is related to the temperature dependence of the dielectric constant
of mixed-stack organic crystals.Comment: 4 pages, 4 figure
X-Band ESR Determination of Dzyaloshinsky-Moriya Interaction in 2D SrCu(BO) System
X-band ESR measurements on a single crystal of SrCu(BO) system in
a temperature range between 10 K and 580 K are presented. The temperature and
angular dependence of unusually broad ESR spectra can be explained by the
inclusion of antisymmetric Dzyaloshinsky-Moriya (DM) interaction, which yields
by far the largest contribution to the linewidth. However, the well-accepted
picture of only out-of-plane interdimer DM vectors is not sufficient for
explanation of the observed angular dependence. In order to account for the
experimental linewidth anisotropy we had to include sizable in-plane components
of interdimer as well as intradimer DM interaction in addition to the
out-of-plane interdimer one. The nearest-neighbor DM vectors lie perpendicular
to crystal anisotropy c-axis due to crystal symmetry. We also emphasize that
above the structural phase transition occurring at 395 K dynamical mechanism
should be present allowing for instantaneous DM interactions. Moreover, the
linewidth at an arbitrary temperature can be divided into two contributions;
namely, the first part arising from spin dynamics governed by the spin
Hamiltonian of the system and the second part due to significant spin-phonon
coupling. The nature of the latter mechanism is attributed to phonon-modulation
of the antisymmetric interaction, which is responsible for the observed linear
increase of the linewidth at high temperatures.Comment: 17 pages, 4 figures, submitted to PR
Solitonic approach to the dimerization problem in correlated one-dimensional systems
Using exact diagonalizations we consider self-consistently the lattice
distortions in odd Peierls-Hubbard and spin-Peierls periodic rings in the
adiabatic harmonic approximation. From the tails of the inherent spin soliton
the dimerization d_\infty of regular even rings is found by extrapolations to
infinite ring lengths. Considering a wide region of electron-electron onsite
interaction values U>0 compared with the band width 4t_0 at intermediately
strong electron-phonon interaction g, known relationships obtained by other
methods are reproduced and/or refined within one unified approach: such as the
maximum of d_\infty at U \simeq 3 t_0 for g \simeq 0.5 and its shift to zero
for g \to g_c \approx 0.7. The hyperbolic tangent shape of the spin soliton is
retained for any U and g <~ 0.6. In the spin-Peierls limit the d_\infty are
found to be in agreement with results of DMRG computations.Comment: 4 pages, 4 figures, Physical Review B, Rapid Communications, v. 56
(1997) accepte
Nonlinear optical response and spin-charge separation in one-dimensional Mott insulators
We theoretically study the nonlinear optical response and photoexcited states
of the Mott insulators. The nonlinear optical susceptibility \chi^(3) is
calculated by using the exact diagonalization technique on small clusters. From
the systematic study of the dependence of \chi^(3) on dimensionality, we find
that the spin-charge separation plays a crucial role in enhancing \chi^(3) in
the one-dimensional (1D) Mott insulators. Based on this result, we propose a
holon-doublon model, which describes the nonlinear response in the 1D Mott
insulators. These findings show that the spin-charge separation will become a
key concept of optoelectronic devices.Comment: 5 pages with 3 figures, to appear in PRB RC, 15 August 200
Nonlinear Optical Response in two-dimensional Mott Insulators
We study the third-order nonlinear optical susceptibility and
photoexcited states of two-dimensional (2D) Mott insulators by using an
effective model in the strong-coupling limit of a half-filled Hubbard model. In
the numerically exact diagonalization calculations on finite-size clusters, we
find that the coupling of charge and spin degrees of freedom plays a crucial
role in the distribution of the dipole-allowed states with odd parity and the
dipole-forbidden states with even parity in the photoexcited states. This is in
contrast with the photoexcited states in one dimension, where the charge and
spin degrees of freedom are decoupled. In the third-harmonic generation (THG)
spectrum, main contribution is found to come from the process of three-photon
resonance associated with the odd-parity states. As a result, the two-photon
resonance process is less pronounced in the THG spectrum. The calculated THG
spectrum is compared with recent experimental data. We also find that
with cross-polarized configuration of pump and probe photons shows
spectral distributions similar to with co-polarized configuration,
although the weight is small. These findings will help the analyses of the
experimental data of in the 2D Mott insulators.Comment: 9 pages,5 figures,RevTeX
Dynamical Correlation Functions using the Density Matrix Renormalization Group
The density matrix renormalization group (DMRG) method allows for very
precise calculations of ground state properties in low-dimensional strongly
correlated systems. We investigate two methods to expand the DMRG to
calculations of dynamical properties. In the Lanczos vector method the DMRG
basis is optimized to represent Lanczos vectors, which are then used to
calculate the spectra. This method is fast and relatively easy to implement,
but the accuracy at higher frequencies is limited. Alternatively, one can
optimize the basis to represent a correction vector for a particular frequency.
The correction vectors can be used to calculate the dynamical correlation
functions at these frequencies with high accuracy. By separately calculating
correction vectors at different frequencies, the dynamical correlation
functions can be interpolated and pieced together from these results. For
systems with open boundaries we discuss how to construct operators for specific
wavevectors using filter functions.Comment: minor revision, 10 pages, 15 figure
Correlation Effect on Peierls Transition
The effect of correlation on Peierls transition, which is accompanied by a
dimerization, t_d, of a bond alternation for transfer energy, has been examined
for a half-filled one-dimensional electron system with on-site repulsive
interaction (U). By applying the renormalization group method to the
interaction of the bosonized Hamiltonian, the dimerization has been calculated
variationally and self-consistently with a fixed electron-phonon coupling
constant (\lambda) and it is shown that t_d takes a maximum as a function of U.
The result is examined in terms of charge gap and spin gap and is compared with
that of the numerical simulation by Hirsch [Phys. Rev. Lett 51 (1983) 296].
Relevance to the spin Peierls transition in organic conductors is discussed.Comment: 4 pages, 4 figures, to be published in J. Phys. Soc. Jpn. 71 No.3
(2002
Molecular crystal approach for pi-conjugated polymers: from PPP Hamiltonian to Holstein model for polaron states
Starting from the -electron Pariser-Parr-Pople (PPP) Hamiltonian which
includes both strong electron-phonon and electron-electron interactions, we
propose some strongly correlated wave functions of increasing quality for the
ground state of conjugated polymers. These wavefunctions are built by combining
different finite sets of local configurations extended at most over two
nearest-neighbour monomers. With this picture, the doped case with one
additional particle is expressed in terms of quasi-particle. Thus, the polaron
formation problem goes back to the study of a Holstein like model.Comment: 27 pages, 6 eps figs, Revtex; enlarged version. Submitted to Journal
of Physics: Condensed Matte
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