2,973 research outputs found
High order Chin actions in path integral Monte Carlo
High order actions proposed by Chin have been used for the first time in path
integral Monte Carlo simulations. Contrarily to the Takahashi-Imada action,
which is accurate to fourth order only for the trace, the Chin action is fully
fourth order, with the additional advantage that the leading fourth and sixth
order error coefficients are finely tunable. By optimizing two free parameters
entering in the new action we show that the time step error dependence achieved
is best fitted with a sixth order law. The computational effort per bead is
increased but the total number of beads is greatly reduced, and the efficiency
improvement with respect to the primitive approximation is approximately a
factor of ten. The Chin action is tested in a one-dimensional harmonic
oscillator, a H drop, and bulk liquid He. In all cases a sixth-order
law is obtained with values of the number of beads that compare well with the
pair action approximation in the stringent test of superfluid He.Comment: 19 pages, 8 figure
Hamiltonian decomposition of K∗n, patterns with distinct differences, and Tuscan squares
AbstractThis paper presents a few constructions for the decomposition of the complete directed graph on n vertices into n Hamiltonian paths. Some of the constructions will apply for even n and others to odd n. The constructions will be obtained from some patterns with distinct differences. The constructions will be exhibited by squares (called Tuscan squares) which sometimes are Latin squares (called Roman squares), and sometimes are not Latin. These squares have some special properties which are discussed in this paper
Higher order and infinite Trotter-number extrapolations in path integral Monte Carlo
Improvements beyond the primitive approximation in the path integral Monte
Carlo method are explored both in a model problem and in real systems. Two
different strategies are studied: the Richardson extrapolation on top of the
path integral Monte Carlo data and the Takahashi-Imada action. The Richardson
extrapolation, mainly combined with the primitive action, always reduces the
number-of-beads dependence, helps in determining the approach to the dominant
power law behavior, and all without additional computational cost. The
Takahashi-Imada action has been tested in two hard-core interacting quantum
liquids at low temperature. The results obtained show that the fourth-order
behavior near the asymptote is conserved, and that the use of this improved
action reduces the computing time with respect to the primitive approximation.Comment: 19 pages, RevTex, to appear in J. Chem. Phy
One-dimensional Ising ferromagnet frustrated by long-range interactions at finite temperatures
We consider a one-dimensional lattice of Ising-type variables where the
ferromagnetic exchange interaction J between neighboring sites is frustrated by
a long-ranged anti-ferromagnetic interaction of strength g between the sites i
and j, decaying as |i-j|^-alpha, with alpha>1. For alpha smaller than a certain
threshold alpha_0, which is larger than 2 and depends on the ratio J/g, the
ground state consists of an ordered sequence of segments with equal length and
alternating magnetization. The width of the segments depends on both alpha and
the ratio J/g. Our Monte Carlo study shows that the on-site magnetization
vanishes at finite temperatures and finds no indication of any phase
transition. Yet, the modulation present in the ground state is recovered at
finite temperatures in the two-point correlation function, which oscillates in
space with a characteristic spatial period: The latter depends on alpha and J/g
and decreases smoothly from the ground-state value as the temperature is
increased. Such an oscillation of the correlation function is exponentially
damped over a characteristic spatial scale, the correlation length, which
asymptotically diverges roughly as the inverse of the temperature as T=0 is
approached. This suggests that the long-range interaction causes the Ising
chain to fall into a universality class consistent with an underlying
continuous symmetry. The e^(Delta/T)-temperature dependence of the correlation
length and the uniform ferromagnetic ground state, characteristic of the g=0
discrete Ising symmetry, are recovered for alpha > alpha_0.Comment: 12 pages, 7 figure
Bond-disordered spin systems: Theory and application to doped high-Tc compounds
We examine the stability of magnetic order in a classical Heisenberg model
with quenched random exchange couplings. This system represents the spin
degrees of freedom in high- compounds with immobile dopants.
Starting from a replica representation of the nonlinear -model, we
perform a renormalization-group analysis. The importance of cumulants of the
disorder distribution to arbitrarily high orders necessitates a functional
renormalization scheme. From the renormalization flow equations we determine
the magnetic correlation length numerically as a function of the impurity
concentration and of temperature. From our analysis follows that
two-dimensional layers can be magnetically ordered for arbitrarily strong but
sufficiently diluted defects. We further consider the dimensional crossover in
a stack of weakly coupled layers. The resulting phase diagram is compared with
experimental data for LaSrCuO.Comment: 12 pages, 5 figure
ARPES and NMTO Wannier Orbital Theory of LiMoO - Implications for Unusually Robust Quasi-One Dimensional Behavior
We present the results of a combined study by band theory and angle resolved
photoemission spectroscopy (ARPES) of the purple bronze,
LiMoO. Structural and electronic origins of its unusually
robust quasi-one dimensional (quasi-1D) behavior are investigated in detail.
The band structure, in a large energy window around the Fermi energy, is
basically 2D and formed by three Mo -like extended Wannier orbitals,
each one giving rise to a 1D band running at a 120 angle to the two
others. A structural "dimerization" from to gaps
the and bands while leaving the bands metallic in the gap, but
resonantly coupled to the gap edges and, hence, to the other directions. The
resulting complex shape of the quasi-1D Fermi surface (FS), verified by our
ARPES, thus depends strongly on the Fermi energy position in the gap, implying
a great sensitivity to Li stoichiometry of properties dependent on the FS, such
as FS nesting or superconductivity. The strong resonances prevent either a
two-band tight-binding model or a related real-space ladder picture from giving
a valid description of the low-energy electronic structure. We use our extended
knowledge of the electronic structure to newly advocate for framing
LiMoO as a weak-coupling material and in that framework can
rationalize both the robustness of its quasi-1D behavior and the rather large
value of its Luttinger liquid (LL) exponent . Down to a temperature of
6K we find no evidence for a theoretically expected downward
renormalization of perpendicular single particle hopping due to LL fluctuations
in the quasi-1D chains.Comment: 53 pages, 17 Figures, 6 year
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