1,067 research outputs found
Ground states of a frustrated quantum spin chain with long-range interactions
The ground state of a spin-1/2 Heisenberg chain with both frustration and
long-range interactions is studied using Lanczos exact diagonalization. The
evolution of the well known dimerization transition of the system with
short-range frustrated interactions (the J1-J2 chain) is investigated in the
presence of additional unfrustrated interactions decaying with distance as
1/r^a. It is shown that the continuous (infinite-order) dimerization transition
develops into a first-order transition between a long-range ordered
antiferromagnetic state and a state with coexisting dimerization and critical
spin correlations at wave-number k=\pi/2. The relevance of the model to real
systems is discussed.Comment: 4 pages, 5 figures, final published versio
Ground state projection of quantum spin systems in the valence bond basis
A Monte Carlo method for quantum spin systems is formulated in the basis of
valence bond (singlet pair) states. The non-orthogonality of this basis allows
for an efficient importance-sampled projection of the ground state out of an
arbitrary state. The method provides access to resonating valence-bond physics,
enables a direct improved estimator for the singlet-triplet gap, and extends
the class of models that can be studied without negative-sign problems. As a
demonstration, the valence bond distribution in the ground state of the 2D
Heisenberg antiferromagnet is calculated. Generalizations of the method to
fermion systems are also discussed.Comment: 4+ pages, accepted for publication in Phys. Rev. Let
Master equation approach to computing RVB bond amplitudes
We describe a "master equation" analysis for the bond amplitudes h(r) of an
RVB wavefunction. Starting from any initial guess, h(r) evolves (in a manner
dictated by the spin hamiltonian under consideration) toward a steady-state
distribution representing an approximation to the true ground state. Unknown
transition coefficients in the master equation are treated as variational
parameters. We illustrate the method by applying it to the J1-J2
antiferromagnetic Heisenberg model. Without frustration (J2=0), the amplitudes
are radially symmetric and fall off as 1/r^3 in the bond length. As the
frustration increases, there are precursor signs of columnar or plaquette VBS
order: the bonds preferentially align along the axes of the square lattice and
weight accrues in the nearest-neighbour bond amplitudes. The Marshall sign rule
holds over a large range of couplings, J2/J1 < 0.418. It fails when the r=(2,1)
bond amplitude first goes negative, a point also marked by a cusp in the ground
state energy. A nonrigourous extrapolation of the staggered magnetic moment
(through this point of nonanalyticity) shows it vanishing continuously at a
critical value J2/J1 = 0.447. This may be preempted by a first-order transition
to a state of broken translational symmetry.Comment: 8 pages, 7 figure
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
Impurity-induced frustration in correlated oxides
Using the example of Zn-doped La2CuO4, we demonstrate that a spinless
impurity doped into a non-frustrated antiferromagnet can induce substantial
frustrating interactions among the spins surrounding it. This counterintuitive
result is the key to resolving discrepancies between experimental data and
earlier theories. Analytic and quantum Monte Carlo studies of the
impurity-induced frustration are in a close accord with each other and
experiments. The mechanism proposed here should be common to other correlated
oxides as well.Comment: 4 pages, updated figures, accepted versio
Magnetic ordering in a doped frustrated spin-Peierls system
Based on a model of a quasi-one dimensional spin-Peierls system doped with
non-magnetic impurities, an effective two-dimensional Hamiltonian of randomly
distributed S=1/2 spins interacting via long-range pair-wise interaction is
studied using a stochastic series expansion quantum Monte Carlo method. The
susceptibility shows Curie-like behavior at the lowest temperatures reached
although the staggered magnetisation is found to be finite for . The
doping dependance of the corresponding three-dimensional Neel temperature is
also computed.Comment: Published version, 4 pages, 5 figure
Properties of Resonating-Valence-Bond Spin Liquids and Critical Dimer Models
We use Monte Carlo simulations to study properties of Anderson's
resonating-valence-bond (RVB) spin-liquid state on the square lattice (i.e.,
the equal superposition of all pairing of spins into nearest-neighbor singlet
pairs) and compare with the classical dimer model (CDM). The latter system also
corresponds to the ground state of the Rokhsar-Kivelson quantum dimer model at
its critical point. We find that although spin-spin correlations decay
exponentially in the RVB, four-spin valence-bond-solid (VBS) correlations are
critical, qualitatively like the well-known dimer-dimer correlations of the
CDM, but decaying more slowly (as with , compared with
for the CDM). We also compute the distribution of monomer (defect) pair
separations, which decay by a larger exponent in the RVB than in the CDM. We
further study both models in their different winding number sectors and
evaluate the relative weights of different sectors. Like the CDM, all the
observed RVB behaviors can be understood in the framework of a mapping to a
"height" model characterized by a gradient-squared stiffness constant . Four
independent measurements consistently show a value , with the same kinds of numerical evaluations of give
results in agreement with the rigorously known value . The
background of a nonzero winding number gradient introduces spatial
anisotropies and an increase in the effective K, both of which can be
understood as a consequence of anharmonic terms in the height-model free
energy, which are of relevance to the recently proposed scenario of "Cantor
deconfinement" in extended quantum dimer models. We also study ensembles in
which fourth-neighbor (bipartite) bonds are allowed, at a density controlled by
a tunable fugacity, resulting (as expected) in a smooth reduction of K.Comment: 26 pages, 21 figures. v3: final versio
Two-Dimensional Quantum XY Model with Ring Exchange and External Field
We present the zero-temperature phase diagram of a square lattice quantum
spin 1/2 XY model with four-site ring exchange in a uniform external magnetic
field. Using quantum Monte Carlo techniques, we identify various quantum phase
transitions between the XY-order, striped or valence bond solid, staggered Neel
antiferromagnet and fully polarized ground states of the model. We find no
evidence for a quantum spin liquid phase.Comment: 4 pages, 4 figure
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
Effects of intrabilayer coupling on the magnetic properties of YBaCuO
A two-layer Heisenberg antiferromagnet is studied as a model of the bilayer
cuprate YBaCuO. Quantum Monte Carlo results are presented for the
temperature dependence of the spin correlation length, the static structure
factor, the magnetic susceptibility, and the Cu NMR spin-echo decay rate
. As expected, when the ratio of the intrabilayer and
in-plane coupling strengths is small, increasing pushes the system deeper
inside the renormalized classical regime. Even for as small as
the correlations are considerably enhanced at temperatures as high as . This has a significant effect on , and it is
suggested that measurements of this quantity at high temperatures can reveal
the strength of the intrabilayer coupling in YBaCuO.Comment: 10 pages (Revtex) + 5 uuencoded ps figures. To appear in Phys. Rev.
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