662 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
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
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
Reply to the Comment by Sandvik, Sengupta, and Campbell on ``Ground State Phase Diagram of a Half-Filled One-Dimensional Extended Hubbard Model''
In their Comment (see cond-mat/0301237), Sandvik, Sengupta, and Campbell
present some numerical evidences to support the existence of an extended
bond-order-wave (BOW) phase at couplings (U,V) weaker than a tricritical point
(U_t,V_t) in the ground state phase diagram of the one-dimensional half-filled
U-V Hubbard model. They claim that their results do not agree with the phase
diagram proposed in my Letter (cond-mat/0204244), which shows a BOW phase for
couplings stronger than the critical point only. However, I argue here that
their results are not conclusive and do not refute the phase diagram described
in the Letter.Comment: 1 page, published versio
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
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