790 research outputs found
Comment on ``Quantum Phase Transition of the Randomly Diluted Heisenberg Antiferromagnet on a Square Lattice''
In Phys. Rev. Lett. 84, 4204 (2000) (cond-mat/9905379), Kato et al. presented
quantum Monte Carlo results indicating that the critical concentration of
random non-magnetic sites in the two-dimensional antiferromagnetic Heisenberg
model equals the classical percolation density; pc=0.407254. The data also
suggested a surprising dependence of the critical exponents on the spin S of
the magnetic sites, with a gradual approach to the classical percolation
exponents as S goes to infinity. I here argue that the exponents in fact are
S-independent and equal to those of classical percolation. The apparent
S-dependent behavior found by Kato et al. is due to temperature effects in the
simulations as well as a quantum effect that masks the true asymptotic scaling
behavior for small lattices.Comment: Comment on Phys. Rev. Lett. 84, 4204 (2000), by K. Kato et al.; 1
page, 1 figur
Spin nematic ground state of the triangular lattice S=1 biquadratic model
Motivated by the spate of recent experimental and theoretical interest in
Mott insulating S=1 triangular lattice magnets, we consider a model S=1
Hamiltonian on a triangular lattice interacting with rotationally symmetric
biquadratic interactions. We show that the partition function of this model can
be expressed in terms of configurations of three colors of tightly-packed,
closed loops with {\em non-negative} weights, which allows for efficient
quantum Monte Carlo sampling on large lattices. We find the ground state has
spin nematic order, i.e. it spontaneously breaks spin rotation symmetry but
preserves time reversal symmetry. We present accurate results for the
parameters of the low energy field theory, as well as finite-temperature
thermodynamic functions
Monte Carlo Simulations of Quantum Spin Systems in the Valence Bond Basis
We discuss a projector Monte Carlo method for quantum spin models formulated
in the valence bond basis, using the S=1/2 Heisenberg antiferromagnet as an
example. Its singlet ground state can be projected out of an arbitrary basis
state as the trial state, but a more rapid convergence can be obtained using a
good variational state. As an alternative to first carrying out a time
consuming variational Monte Carlo calculation, we show that a very good trial
state can be generated in an iterative fashion in the course of the simulation
itself. We also show how the properties of the valence bond basis enable
calculations of quantities that are difficult to obtain with the standard basis
of Sz eigenstates. In particular, we discuss quantities involving
finite-momentum states in the triplet sector, such as the dispersion relation
and the spectral weight of the lowest triplet.Comment: 15 pages, 7 figures, for the proceedings of "Computer Simulation
Studies in Condensed Matter Physics XX
Comment on "Evidence for nontrivial ground-state structure of 3d +/- J spin glasses"
In a recent Letter [Europhys. Lett. 40, 429 (1997)], Hartmann presented
results for the structure of the degenerate ground states of the
three-dimensional +/- J spin glass model obtained using a genetic algorithm. In
this Comment, I argue that the method does not produce the correct
thermodynamic distribution of ground states and therefore gives erroneous
results for the overlap distribution. I present results of simulated annealing
calculations using different annealing rates for cubic lattices with
N=4*4*4spins. The disorder-averaged overlap distribution exhibits a significant
dependence on the annealing rate, even when the energy has converged. For fast
annealing, moments of the distribution are similar to those presented by
Hartmann. However, as the annealing rate is lowered, they approach the results
previously obtained using a multi-canonical Monte Carlo method. This shows
explicitly that care must be taken not only to reach states with the lowest
energy but also to ensure that they obey the correct thermodynamic
distribution, i.e., that the probability is the same for reaching any of the
ground states.Comment: 2 pages, Revtex, 1 PostScript figur
Stochastic Cluster Series expansion for quantum spin systems
In this paper we develop a cluster-variant of the Stochastic Series expansion
method (SCSE). For certain systems with longer-range interactions the SCSE is
considerably more efficient than the standard implementation of the Stochastic
Series Expansion (SSE), at low temperatures. As an application of this method
we calculated the T=0-conductance for a linear chain with a (diagonal) next
nearest neighbor interaction.Comment: 5 pages, 7 figure
Spin dynamics of SrCuO and the Heisenberg ladder
The Heisenberg antiferromagnet in the ladder geometry is studied as a
model for the spin degrees of freedom of SrCuO. The susceptibility and
the spin echo decay rate are calculated using a quantum Monte Carlo technique,
and the spin-lattice relaxation rate is obtained by maximum entropy analytic
continuation of imaginary time correlation functions. All calculated quantities
are in reasonable agreement with experimental results for SrCuO if the
exchange coupling K, i.e. significantly smaller than in
high-T cuprates.Comment: 11 pages (Revtex) + 3 uuencoded ps files. To appear in Phys. Rev. B,
Rapid Com
Order-Disorder Transition in a Two-Layer Quantum Antiferromagnet
We have studied the antiferromagnetic order -- disorder transition occurring
at in a 2-layer quantum Heisenberg antiferromagnet as the inter-plane
coupling is increased. Quantum Monte Carlo results for the staggered structure
factor in combination with finite-size scaling theory give the critical ratio
between the inter-plane and in-plane coupling constants.
The critical behavior is consistent with the 3D classical Heisenberg
universality class. Results for the uniform magnetic susceptibility and the
correlation length at finite temperature are compared with recent predictions
for the 2+1-dimensional nonlinear -model. The susceptibility is found
to exhibit quantum critical behavior at temperatures significantly higher than
the correlation length.Comment: 11 pages (5 postscript figures available upon request), Revtex 3.
Susceptibility of the 2D S=1/2 Heisenberg antiferromagnet with an impurity
We use a quantum Monte Carlo method (stochastic series expansion) to study
the effects of a magnetic or nonmagnetic impurity on the magnetic
susceptibility of the two-dimensional Heisenberg antiferromagnet. At low
temperatures, we find a log-divergent contribution to the transverse
susceptibility. We also introduce an effective few-spin model that can
quantitatively capture the differences between magnetic and nonmagnetic
impurities at high and intermediate temperatures.Comment: 5 pages, 4 figures, v2: Updated data in figures, minor changes in
text, v3: Final version, cosmetic change
Critical temperature and the transition from quantum to classical order parameter fluctuations in the three-dimensional Heisenberg antiferromagnet
We present results of extensive quantum Monte Carlo simulations of the
three-dimensional (3D) S=1/2 Heisenberg antiferromagnet. Finite-size scaling of
the spin stiffness and the sublattice magnetization gives the critical
temperature Tc/J = 0.946 +/- 0.001. The critical behavior is consistent with
the classical 3D Heisenberg universality class, as expected. We discuss the
general nature of the transition from quantum mechanical to classical (thermal)
order parameter fluctuations at a continuous Tc > 0 phase transition.Comment: 5 pages, Revtex, 4 PostScript figures include
- …