1,385 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
Accessing the dynamics of large many-particle systems using Stochastic Series Expansion
The Stochastic Series Expansion method (SSE) is a Quantum Monte Carlo (QMC)
technique working directly in the imaginary time continuum and thus avoiding
"Trotter discretization" errors. Using a non-local "operator-loop update" it
allows treating large quantum mechanical systems of many thousand sites. In
this paper we first give a comprehensive review on SSE and present benchmark
calculations of SSE's scaling behavior with system size and inverse
temperature, and compare it to the loop algorithm, whose scaling is known to be
one of the best of all QMC methods. Finally we introduce a new and efficient
algorithm to measure Green's functions and thus dynamical properties within
SSE.Comment: 11 RevTeX pages including 7 figures and 5 table
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.
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
Comment on ``Ground State Phase Diagram of a Half-Filled One-Dimensional Extended Hubbard Model''
In Phys. Rev. Lett. 89, 236401 (2002), Jeckelmann argued that the recently
discovered bond-order-wave (BOW) phase of the 1D extended Hubbard model does
not have a finite extent in the (U,V) plane, but exists only on a segment of a
first-order SDW-CDW phase boundary. We here present quantum Monte Carlo result
of higher precision and for larger system sizes than previously and reconfirm
that the BOW phase does exist a finite distance away from the phase boundary,
which hence is a BOW-CDW transition curve.Comment: 1 page, 1 figure, v2: final published versio
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
- …