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

LiHoF4_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