19 research outputs found

### Classical spin models and basic magnetic interactions on 1/1-approximant crystals

We study classical spin models on the 1/1 Tsai-type approximant lattice using
Monte Carlo and mean-field methods. Our aim is to understand whether the phase
diagram differences between Gd- and Tb-based approximants can be attributed to
anisotropy induced by the crystal-electric field. To address this question, we
treat Gd ions as Heisenberg spins and Tb ions as Ising spins. Additionally, we
consider the presence of the RKKY interaction to replicate the experimentally
observed correlation between magnetic properties and electron concentration.
Surprisingly, our findings show that the transition between ferromagnetic and
antiferromagnetic order remains unaltered by the anisotropy, even when
accounting for the dipole interaction. We conclude that a more comprehensive
model, extending beyond the free-electron gas RKKY interaction, is likely
required to fully understand the distinctions between Gd- and Tb-based
approximants. Our work represents a systematic exploration of the impact of
anisotropy on the ground-state properties of classical spin models in
quasicrystal approximants.Comment: 15 figures, 10 page

### Local density approximation for confined bosons in an optical lattice

We investigate local and global properties of the one-dimensional
Bose-Hubbard model with an external confining potential, describing an atomic
condensate in an optical lattice. Using quantum Monte Carlo techniques we
demonstrate that a local-density approximation, which relates the unconfined
and the confined model, yields quantitatively correct results in most of the
interesting parameter range. We also examine claims of universal behavior in
the confined system, and demonstrate the origin of a previously calculated fine
structure in the experimentally accessible momentum distribution.Comment: 7 pages, 11 figures; Section III updated and references adde

### Reduction of the sign problem using the meron-cluster approach

The sign problem in quantum Monte Carlo calculations is analyzed using the
meron-cluster solution. The concept of merons can be used to solve the sign
problem for a limited class of models. Here we show that the method can be used
to \textit{reduce} the sign problem in a wider class of models. We investigate
how the meron solution evolves between a point in parameter space where it
eliminates the sign problem and a point where it does not affect the sign
problem at all. In this intermediate regime the merons can be used to reduce
the sign problem. The average sign still decreases exponentially with system
size and inverse temperature but with a different prefactor. The sign exhibits
the slowest decrease in the vicinity of points where the meron-cluster solution
eliminates the sign problem. We have used stochastic series expansion quantum
Monte Carlo combined with the concept of directed loops.Comment: 8 pages, 9 figure

### Ground state of the random-bond spin-1 Heisenberg chain

Stochastic series expansion quantum Monte Carlo is used to study the ground
state of the antiferromagnetic spin-1 Heisenberg chain with bond disorder.
Typical spin- and string-correlations functions behave in accordance with
real-space renormalization group predictions for the random-singlet phase. The
average string-correlation function decays algebraically with an exponent of
-0.378(6), in very good agreement with the prediction of $-(3-\sqrt{5})/2\simeq
-0.382$, while the average spin-correlation function is found to decay with an
exponent of about -1, quite different from the expected value of -2. By
implementing the concept of directed loops for the spin-1 chain we show that
autocorrelation times can be reduced by up to two orders of magnitude.Comment: 9 pages, 10 figure

### LiHoF$_4$: Cuboidal Demagnetizing Factor in an Ising Ferromagnet

The demagnetizing factor has an important effect on the physics of
ferromagnets. For cuboidal samples it depends on susceptibility and the
historic problem of determining this function continues to generate theoretical
and experimental challenges. To test a recent theory, we measure the magnetic
susceptibility of the Ising dipolar ferromagnet LiHoF$_4$, using samples of
varying aspect ratio, and we reconsider the demagnetizing transformation
necessary to obtain the intrinsic material susceptibility. Our experimental
results confirm that the microscopic details of the material significantly
affect the transformation, as predicted. In particular, we find that the
uniaxial Ising spins require a demagnetizing transformation that differs from
the one needed for Heisenberg spins and that use of the wrong demagnetizing
transformation would result in unacceptably large errors in the measured
physical properties of the system. Our results further shed light on the origin
of the mysterious `flat' susceptibility of ordered ferromagnets by
demonstrating that the intrinsic susceptibility of the ordered ferromagnetic
phase is infinite, regardless of sample shape.Comment: 8 pages, 4 figure

### A Two-dimensional Infinte System Density Matrix Renormalization Group Algorithm

It has proved difficult to extend the density matrix renormalization group
technique to large two-dimensional systems. In this Communication I present a
novel approach where the calculation is done directly in two dimensions. This
makes it possible to use an infinite system method, and for the first time the
fixed point in two dimensions is studied. By analyzing several related blocking
schemes I find that there exists an algorithm for which the local energy
decreases monotonically as the system size increases, thereby showing the
potential feasibility of this method.Comment: 5 pages, 6 figure