114 research outputs found
A New Method of the High Temperature Series Expansion
We formulate a new method of performing high-temperature series expansions
for the spin-half Heisenberg model or, more generally, for SU() Heisenberg
model with arbitrary . The new method is a novel extension of the
well-established finite cluster method. Our method emphasizes hidden
combinatorial aspects of the high-temperature series expansion, and solves the
long-standing problem of how to efficiently calculate correlation functions of
operators acting at widely separated sites. Series coefficients are expressed
in terms of cumulants, which are shown to have the property that all deviations
from the lowest-order nonzero cumulant can be expressed in terms of a
particular kind of moment expansion. These ``quasi-moments'' can be written in
terms of corresponding ``quasi-cumulants'', which enable us to calculate
higher-order terms in the high-temperature series expansion. We also present a
new technique for obtaining the low-order contributions to specific heat from
finite clusters.Comment: 20 pages, 30 figures, to appear in J. Stat. Phy
Grand canonical Gutzwiller approximation for magnetic inhomogeneous systems
The Gutzwiller approximation (GA) for Gutzwiller-projected grand canonical
wave functions with fugacity factors is investigated in detail. Our systems in
general contain inhomogeneity and local magnetic moments. In deriving
renormalization formulae, we also derive or estimate terms of higher powers of
intersite contractions neglected in the conventional GA. We examine several
different constraints, i.e., local/global spin-dependent/independent
particle-number conservation. Out of the four, the local spin-dependent
constraint seems the most promising at present. An improved GA derived from it
agrees with the variational Monte Carlo method better than the conventional GA
does. The corrections to the conventional GA can be interpreted as two-site
correlation including the phase difference of configurations. Furthermore,
projected quasi-particle excited states are orthogonal to each other within the
GA. Using these states, spectral weights are calculated. We show that asymmetry
between electron addition and removal spectra can appear by taking into account
the higher powers of the intersite contractions in the case of the d-wave
superconductors and the Fermi sea; the addition is smaller than the removal.
However, the asymmetry is quite weak especially near the Fermi level. In
contrast, projected s-wave superconductors can have the opposite asymmetry
(addition larger than removal) especially near the Fermi level. In addition,
formulae from the other three constraints are also derived, which may be useful
depending on purposes.Comment: 18 pages. 8 figures added. Sec.II B, Sec.III F G H, Sec.IV G mainly
revise
High Temperature Expansion for the SU(n) Heisenberg Model in One Dimension
Thermodynamic properties of the SU() Heisenberg model in one dimension is
studied by means of high-temperature expansion for arbitrary . The specific
heat up to and the correlation function up to are derived with being the antiferromagnetic exchange in
units of temperature. It is found for that the specific heat shows a
shoulder in the high-temperature side of a peak. The origin of this structure
is clarified by deriving the temperature dependence of the correlation
function. With decreasing temperature, the short-range correlation with
two-site periodicity develops first, and then another correlation with -site
periodicity at lower temperature. This behavior is in contrast to that of the
inverse square interaction model, where the specific heat shows a single peak
according to the exact solution. Our algorithm has an advantage that neither
computational time nor memory depends on the multiplicity per site; the
series coefficients are obtained as explicit functions of .Comment: 4 pages including 4 PS-figures, submitted to J. Phys. Soc. Jp
Renormalization of transition matrix elements of particle number operators due to strong electron correlation
Renormalization of non-magnetic and magnetic impurities due to electron
double occupancy prohibition is derived analytically by an improved Gutzwiller
approximation. Non-magnetic impurities are effectively weakened by the same
renormalization factor as that for the hopping amplitude, whereas magnetic
impurities are strengthened by the square root of the spin-exchange
renormalization factor, in contrast to results by the conventional Gutzwiller
approximation. We demonstrate it by showing that transition matrix elements of
number operators between assumed excited states and between an assumed ground
state and excited states are renormalized differently than diagonal matrix
elements. Deviation from such simple renormalization with a factor is also
discussed. In addition, as related calculation, we correct an error in
treatment of renormalization of charge interaction in the literature. Namely,
terms from the second order of the transition matrix elements are strongly
suppressed. Since all these results do not depend on the signs of impurity
potential or charge interaction parameter, they are valid both in attractive
and repulsive cases.Comment: 12 page
The cluster glass state in the two-dimensional extended t-J model
The recent observation of an electronic cluster glass state composed of
random domains with unidirectional modulation of charge density and/or spin
density on Bi_{2}Sr_{2}CaCu_{2}O_{8+\delta} reinvigorates the debate of
existence of competing interactions and their importance in high temperature
superconductivity. By using a variational approach, here we show that the
presence of the cluster glass state is actually an inherent nature of the model
based on the antiferromagnetic interaction (J) only, i.e. the well known t-J
model. There is no need yet to introduce a competing interaction to understand
the existence of the cluster glass state. The long-range pairing correlation is
not much influenced by the disorder in the glass state which also has nodes and
linear density of states. In the antinodal region, the spectral weight is
almost completely suppressed. The modulation also produces subgap structures
inside the "coherent" peaks of the local density of states.Comment: 9 pages, 5 figures, submitted to PR
On the evaluation of matrix elements in partially projected wave functions
We generalize the Gutzwiller approximation scheme to the calculation of
nontrivial matrix elements between the ground state and excited states. In our
scheme, the normalization of the Gutzwiller wave function relative to a
partially projected wave function with a single non projected site (the
reservoir site) plays a key role. For the Gutzwiller projected Fermi sea, we
evaluate the relative normalization both analytically and by variational
Monte-Carlo (VMC). We also report VMC results for projected superconducting
states that show novel oscillations in the hole density near the reservoir
site
Thermodynamic properties of ferromagnetic mixed-spin chain systems
Using a combination of high-temperature series expansion, exact
diagonalization and quantum Monte Carlo, we perform a complementary analysis of
the thermodynamic properties of quasi-one-dimensional mixed-spin systems with
alternating magnetic moments. In addition to explicit series expansions for
small spin quantum numbers, we present an expansion that allows a direct
evaluation of the series coefficients as a function of spin quantum numbers.
Due to the presence of excitations of both acoustic and optical nature, the
specific heat of a mixed-spin chain displays a double-peak-like structure,
which is more pronounced for ferromagnetic than for antiferromagnetic
intra-chain exchange. We link these results to an analytically solvable
half-classical limit. Finally, we extend our series expansion to incorporate
the single-ion anisotropies relevant for the molecular mixed-spin ferromagnetic
chain material MnNi(NO)(ethylenediamine), with alternating
spins of magnitude 5/2 and 1. Including a weak inter-chain coupling, we show
that the observed susceptibility allows for an excellent fit, and the
extraction of microscopic exchange parameters.Comment: 8 pages including 7 figures, submitted to Phys. Rev. B; series
extended to 29th. QMC adde
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