1,117 research outputs found
NMR relaxation rates for the spin-1/2 Heisenberg chain
The spin-lattice relaxation rate and the spin echo decay rate
for the spin- antiferromagnetic Heisenberg chain are
calculated using quantum Monte Carlo and maximum entropy analytic continuation.
The results are compared with recent analytical calculations by Sachdev. If the
nuclear hyperfine form factor is strongly peaked around the
predicted low-temperature behavior [, ] extends up to temperatures as high as . If has significant weight for there are large
contributions from diffusive long-wavelength processes not taken into account
in the theory, and very low temperatures are needed in order to observe the
asymptotic forms.Comment: 9 pages, Revtex 3.0, 5 uuencoded ps figures To appear in Phys. Rev.
B, Rapid Com
Stochastic series expansion method with operator-loop update
A cluster update (the ``operator-loop'') is developed within the framework of
a numerically exact quantum Monte Carlo method based on the power series
expansion of exp(-BH) (stochastic series expansion). The method is generally
applicable to a wide class of lattice Hamiltonians for which the expansion is
positive definite. For some important models the operator-loop algorithm is
more efficient than loop updates previously developed for ``worldline''
simulations. The method is here tested on a two-dimensional anisotropic
Heisenberg antiferromagnet in a magnetic field.Comment: 5 pages, 4 figure
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
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
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
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
Multi-critical point in a diluted bilayer Heisenberg quantum antiferromagnet
The S=1/2 Heisenberg bilayer antiferromagnet with randomly removed
inter-layer dimers is studied using quantum Monte Carlo simulations. A
zero-temperature multi-critical point (p*,g*) at the classical percolation
density p=p* and inter-layer coupling g* approximately 0.16 is demonstrated.
The quantum critical exponents of the percolating cluster are determined using
finite-size scaling. It is argued that the associated finite-temperature
quantum critical regime extends to zero inter-layer coupling and could be
relevant for antiferromagnetic cuprates doped with non-magnetic impurities.Comment: 4 pages, 6 figures. v2: only minor changes; accepted for publication
in Phys. Rev. Let
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.
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