115 research outputs found
Critical Behaviour of One-particle Spectral Weights in the Transverse Ising Model
We investigate the critical behaviour of the spectral weight of a single
quasiparticle, one of the key observables in experiment, for the particular
case of the transverse Ising model.Series expansions are calculated for the
linear chain and the square and simple cubic lattices. For the chain model, a
conjectured exact result is discovered. For the square and simple cubic
lattices, series analyses are used to estimate the critical exponents. The
results agree with the general predictions of Sachdev.Comment: 4 pages, 3 figure
Unusual Critical Behavior in a BilinearâBiquadratic Exchange Hamiltonian
We have performed a variety of numerical studies on the general bilinearâbiquadratic spinâ1 Hamiltonian H/J=â N i=1[S i â
S i+1 âβ(S i â
S i+1)2], over the range 0â¤Î˛â¤â. The model is Bethe Ansatz integrable at the special point β=1, where the spectrum is gapless, but is otherwise believed to be nonintegrable. Affleck has predicted that an excitation gap opens up linearly in the vicinity of β=1. Our studies involving spectral excitations (dispersion spectra), scaledâgap, and finiteâsize scaling calculations are not consistent with the Affleck prediction. The situation appears complex, with novel crossover effects occurring in both regimes, ββ\u3e1, complicating the analysis
Exact diagonalization of the S=1/2 Heisenberg antiferromagnet on finite bcc lattices to estimate properties on the infinite lattice
Here we generate finite bipartite body-centred cubic lattices up to 32
vertices. We have studied the spin one half Heisenberg antiferromagnet by
diagonalizing its Hamiltonian on each of the finite lattices and hence
computing its ground state properties. By extrapolation of these data we obtain
estimates of the T = 0 properties on the infinite bcc lattice. Our estimate of
the T = 0 energy agrees to five parts in ten thousand with third order spin
wave and series expansion method estimates, while our estimate of the staggered
magnetization agrees with the spin wave estimate to within a quarter of one
percent.Comment: 16 pages, LaTeX, 1 ps figure, to appear in J.Phys.
Numerical Linked-Cluster Approach to Quantum Lattice Models
We present a novel algorithm that allows one to obtain temperature dependent
properties of quantum lattice models in the thermodynamic limit from exact
diagonalization of small clusters. Our Numerical Linked Cluster (NLC) approach
provides a systematic framework to assess finite-size effects and is valid for
any quantum lattice model. Unlike high temperature expansions (HTE), which have
a finite radius of convergence in inverse temperature, these calculations are
accurate at all temperatures provided the range of correlations is finite. We
illustrate the power of our approach studying spin models on {\it kagom\'e},
triangular, and square lattices.Comment: 4 pages, 5 figures, published versio
Numerical Linked-Cluster Algorithms. I. Spin systems on square, triangular, and kagome lattices
We discuss recently introduced numerical linked-cluster (NLC) algorithms that
allow one to obtain temperature-dependent properties of quantum lattice models,
in the thermodynamic limit, from exact diagonalization of finite clusters. We
present studies of thermodynamic observables for spin models on square,
triangular, and kagome lattices. Results for several choices of clusters and
extrapolations methods, that accelerate the convergence of NLC, are presented.
We also include a comparison of NLC results with those obtained from exact
analytical expressions (where available), high-temperature expansions (HTE),
exact diagonalization (ED) of finite periodic systems, and quantum Monte Carlo
simulations.For many models and properties NLC results are substantially more
accurate than HTE and ED.Comment: 14 pages, 16 figures, as publishe
A Frustrated 3-Dimensional Antiferromagnet: Stacked Layers
We study a frustrated 3D antiferromagnet of stacked layers. The
intermediate 'quantum spin liquid' phase, present in the 2D case, narrows with
increasing interlayer coupling and vanishes at a triple point. Beyond this
there is a direct first-order transition from N{\' e}el to columnar order.
Possible applications to real materials are discussed.Comment: 11 pages,7 figure
Critical exponents of the two-layer Ising model
The symmetric two-layer Ising model (TLIM) is studied by the corner transfer
matrix renormalisation group method. The critical points and critical exponents
are calculated. It is found that the TLIM belongs to the same universality
class as the Ising model. The shift exponent is calculated to be 1.773, which
is consistent with the theoretical prediction 1.75 with 1.3% deviation.Comment: 7 pages, with 10 figures include
Series Expansions for the Massive Schwinger Model in Hamiltonian lattice theory
It is shown that detailed and accurate information about the mass spectrum of
the massive Schwinger model can be obtained using the technique of
strong-coupling series expansions. Extended strong-coupling series for the
energy eigenvalues are calculated, and extrapolated to the continuum limit by
means of integrated differential approximants, which are matched onto a
weak-coupling expansion. The numerical estimates are compared with exact
results, and with finite-lattice results calculated for an equivalent lattice
spin model with long-range interactions. Both the heavy fermion and the light
fermion limits of the model are explored in some detail.Comment: RevTeX, 10 figures, add one more referenc
Convergent expansions for properties of the Heisenberg model for CaVO
We have carried out a wide range of calculations for the Heisenberg
model with nearest- and second-neighbor interactions on a two-dimensional
lattice which describes the geometry of the vanadium ions in the spin-gap
system CaVO. The methods used were convergent high-order perturbation
expansions (``Ising'' and ``Plaquette'' expansions at , as well as
high-temperature expansions) for quantities such as the uniform susceptibility,
sublattice magnetization, and triplet elementary excitation spectrum.
Comparison with the data for CaVO indicates that its magnetic
properties are well described by nearest-neighbor exchange of about 200K in
conjunction with second-neighbor exchange of about 100K.Comment: Uses REVTEX macros. Four pages in two-column format, five postscript
figures. Files packaged using uufile
Ground state parameters, finite-size scaling, and low-temperature properties of the two-dimensional S=1/2 XY model
We present high-precision quantum Monte Carlo results for the S=1/2 XY model
on a two-dimensional square lattice, in the ground state as well as at finite
temperature. The energy, the spin stiffness, the magnetization, and the
susceptibility are calculated and extrapolated to the thermodynamic limit. For
the ground state, we test a variety of finite-size scaling predictions of
effective Lagrangian theory and find good agreement and consistency between the
finite-size corrections for different quantities. The low-temperature behavior
of the susceptibility and the internal energy is also in good agreement with
theoretical predictions.Comment: 6 pages, 8 figure
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