958 research outputs found
The sign problem in Monte Carlo simulations of frustrated quantum spin systems
We discuss the sign problem arising in Monte Carlo simulations of frustrated
quantum spin systems. We show that for a class of ``semi-frustrated'' systems
(Heisenberg models with ferromagnetic couplings along the -axis
and antiferromagnetic couplings in the -plane, for
arbitrary distances ) the sign problem present for algorithms operating in
the -basis can be solved within a recent ``operator-loop'' formulation of
the stochastic series expansion method (a cluster algorithm for sampling the
diagonal matrix elements of the power series expansion of
to all orders). The solution relies on identification of operator-loops which
change the configuration sign when updated (``merons'') and is similar to the
meron-cluster algorithm recently proposed by Chandrasekharan and Wiese for
solving the sign problem for a class of fermion models (Phys. Rev. Lett. {\bf
83}, 3116 (1999)). Some important expectation values, e.g., the internal
energy, can be evaluated in the subspace with no merons, where the weight
function is positive definite. Calculations of other expectation values require
sampling of configurations with only a small number of merons (typically zero
or two), with an accompanying sign problem which is not serious. We also
discuss problems which arise in applying the meron concept to more general
quantum spin models with frustrated interactions.Comment: 13 pages, 16 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
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
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.
Critical exponents of the quantum phase transition in a planar antiferromagnet
We have performed a large scale quantum Monte Carlo study of the quantum
phase transition in a planar spin-1/2 Heisenberg antiferromagnet with CaV4O9
structure. We obtain a dynamical exponent z=1.018+/-0.02. The critical
exponents beta, nu and eta agree within our errors with the classical 3D O(3)
exponents, expected from a mapping to the nonlinear sigma model. This confirms
the conjecture of Chubukov, Sachdev and Ye [Phys. Rev. B 49, 11919 (1994)] that
the Berry phase terms in the planar Heisenberg antiferromagnet are dangerously
irrelevant.Comment: 5 pages including 4 figures; revised version: some minor changes and
added reference
Dynamics of the spin-half Heisenberg chain at intermediate temperatures
Combining high-temperature expansions with the recursion method and quantum
Monte Carlo simulations with the maximum entropy method, we study the dynamics
of the spin-1/2 Heisenberg chain at temperatures above and below the coupling
J. By comparing the two sets of calculations, their relative strengths are
assessed. At high temperatures, we find that there is a low-frequency peak in
the momentum integrated dynamic structure factor, due to diffusive
long-wavelength modes. This peak is rapidly suppressed as the temperature is
lowered below J. Calculation of the complete dynamic structure factor S(k,w)
shows how the spectral features associated with the two-spinon continuum
develop at low temperatures. We extract the nuclear spin-lattice relaxation
rate 1/T1 from the w-->0 limit, and compare with recent experimental results
for Sr2CuO3 and CuGeO3. We also discuss the scaling behavior of the dynamic
susceptibility, and of the static structure factor S(k) and the static
susceptibility X(k). We confirm the asymptotic low-temperature forms
S(pi)~[ln(T)]^(3/2) and X(pi)~T^(-1)[ln(T)]^(1/2), expected from previous
theoretical studies.Comment: 15 pages, Revtex, 14 PostScript figures. 2 new figures and related
discussion of the recursion method at finite temperature adde
Double-layer Heisenberg antiferromagnet at finite temperature: Brueckner Theory and Quantum Monte Carlo simulations
The double-layer Heisenberg antiferromagnet with intra- and inter-layer
couplings and exhibits a zero temperature quantum phase
transition between a quantum disordered dimer phase for and a Neel
phase with long range antiferromagnetic order for , where
and . We consider the behavior of the system at finite
temperature for using two different and complementary approaches;
an analytical Brueckner approximation and numerically exact quantum Monte Carlo
simulations. We calculate the temperature dependent spin excitation spectrum
(including the triplet gap), dynamic and static structure factors, the specific
heat, and the uniform magnetic susceptibility. The agreement between the
analytical and numerical approaches is excellent. For and , our analytical results for the specific heat and the magnetic
susceptibility coincide with those previously obtained within the nonlinear
model approach for . Our quantum Monte Carlo simulations
extend to significantly lower temperatures than previously, allowing us to
obtain accurate results for the asymptotic quantum critical behavior. We also
obtain an improved estimate for the critical coupling: .Comment: 23 pages, 12 figure
High-energy magnon dispersion in the half-filled Hubbard model: A comparison with LaCuO
We use quantum Monte Carlo methods and single-mode approximation to study the
magnon dispersion in the 2D half-filled Hubbard and phonon-coupled Heisenberg
models. We find that in the Hubbard model with , high-energy magnon
dispersion is similar to those observed in inelastic neutron scattering
experiments in . On the other hand, our studies of a 2D
Heisenberg model coupled to dynamic optical bond phonons, fails to reproduce
the experimental dispersion. These results can be interpreted as evidence for
intermediate and charge fluctuations in the cuprate materials
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