15 research outputs found
Finite size and temperature effects in the AF Heisenberg model
The low temperature and large volume effects in the d=2+1 antiferromagnetic
quantum Heisenberg model are dominated by magnon excitations. The leading and
next-to-leading corrections are fully controlled by three physical constants,
the spin stiffness, the spin wave velocity and the staggered magnetization.
Among others, the free energy, the ground state energy, the low lying
excitations, staggered magnetization, staggered and uniform susceptibilities
are studied here. The special limits of very low temperature and infinite
volume are considered also.Comment: 44 pages, LATEX, no figure
Quantum disorder in the two-dimensional pyrochlore Heisenberg antiferromagnet
We present the results of an exact diagonalization study of the spin-1/2
Heisenberg antiferromagnet on a two-dimensional version of the pyrochlore
lattice, also known as the square lattice with crossings or the checkerboard
lattice. Examining the low energy spectra for systems of up to 24 spins, we
find that all clusters studied have non-degenerate ground states with total
spin zero, and big energy gaps to states with higher total spin. We also find a
large number of non-magnetic excitations at energies within this spin gap.
Spin-spin and spin-Peierls correlation functions appear to be short-ranged, and
we suggest that the ground state is a spin liquid.Comment: 7 pages, 11 figures, RevTeX minor changes made, Figure 6 correcte
Exact spectra, spin susceptibilities and order parameter of the quantum Heisenberg antiferromagnet on the triangular lattice
Exact spectra of periodic samples are computed up to .
Evidence of an extensive set of low lying levels, lower than the softest
magnons, is exhibited.
These low lying quantum states are degenerated in the thermodynamic limit;
their symmetries and dynamics as well as their finite-size scaling are strong
arguments in favor of N\'eel order.
It is shown that the N\'eel order parameter agrees with first-order spin-wave
calculations. A simple explanation of the low energy dynamics is given as well
as the numerical determinations of the energies, order parameter and spin
susceptibilities of the studied samples. It is shown how suitable boundary
conditions, which do not frustrate N\'eel order, allow the study of samples
with spins.
A thorough study of these situations is done in parallel with the more
conventional case .Comment: 36 pages, REVTeX 3.0, 13 figures available upon request, LPTL
preprin
Quantum Monte Carlo with Directed Loops
We introduce the concept of directed loops in stochastic series expansion and
path integral quantum Monte Carlo methods. Using the detailed balance rules for
directed loops, we show that it is possible to smoothly connect generally
applicable simulation schemes (in which it is necessary to include
back-tracking processes in the loop construction) to more restricted loop
algorithms that can be constructed only for a limited range of Hamiltonians
(where back-tracking can be avoided). The "algorithmic discontinuities" between
general and special points (or regions) in parameter space can hence be
eliminated. As a specific example, we consider the anisotropic S=1/2 Heisenberg
antiferromagnet in an external magnetic field. We show that directed loop
simulations are very efficient for the full range of magnetic fields (zero to
the saturation point) and anisotropies. In particular for weak fields and
anisotropies, the autocorrelations are significantly reduced relative to those
of previous approaches. The back-tracking probability vanishes continuously as
the isotropic Heisenberg point is approached. For the XY-model, we show that
back-tracking can be avoided for all fields extending up to the saturation
field. The method is hence particularly efficient in this case. We use directed
loop simulations to study the magnetization process in the 2D Heisenberg model
at very low temperatures. For LxL lattices with L up to 64, we utilize the
step-structure in the magnetization curve to extract gaps between different
spin sectors. Finite-size scaling of the gaps gives an accurate estimate of the
transverse susceptibility in the thermodynamic limit: chi_perp = 0.0659 +-
0.0002.Comment: v2: Revised and expanded discussion of detailed balance, error in
algorithmic phase diagram corrected, to appear in Phys. Rev.
Low-energy fixed points of random Heisenberg models
The effect of quenched disorder on the low-energy and low-temperature
properties of various two- and three-dimensional Heisenberg models is studied
by a numerical strong disorder renormalization group method. For strong enough
disorder we have identified two relevant fixed points, in which the gap
exponent, omega, describing the low-energy tail of the gap distribution,
P(Delta) ~ Delta^omega is independent of disorder, the strength of couplings
and the value of the spin. The dynamical behavior of non-frustrated random
antiferromagnetic models is controlled by a singlet-like fixed point, whereas
for frustrated models the fixed point corresponds to a large spin formation and
the gap exponent is given by omega ~ 0. Another type of universality classes is
observed at quantum critical points and in dimerized phases but no infinite
randomness behavior is found, in contrast to one-dimensional models.Comment: 11 pages RevTeX, eps-figs included, language revise