Computing quantum phase transitions

This article first gives a concise introduction to quantum phase transitions, emphasizing similarities with and differences to classical thermal transitions. After pointing out the computational challenges posed by quantum phase transitions, a number of successful computational approaches is discussed. The focus is on classical and quantum Monte Carlo methods, with the former being based on the quantum-to classical mapping while the latter directly attack the quantum problem. These methods are illustrated by several examples of quantum phase transitions in clean and disordered systems.Comment: 99 pages, 15 figures, submitted to Reviews in Computational Chemistr

Application of Local Information Entropy in Cluster Monte Carlo Algorithms

The chapter refers to a modification of the so-called adding probability used in cluster Monte Carlo algorithms. The modification is based on the fact that in real systems, different properties can influence its clusterization. Finally, an additional factor related to property disorder was introduced into the adding probability, which leads to more effective free energy minimization during MC iteration. As a measure of the disorder, we proposed to use a local information entropy. The proposed approach was tested and compared with the classical methods, showing its high efficiency in simulations of multiphase magnetic systems where magnetic anisotropy was used as the property influencing the system clusterization

Sign-problem-free Monte Carlo simulation of certain frustrated quantum magnets

We introduce a Quantum Monte Carlo (QMC) method which efficiently simulates in a sign-problem-free way a broad class of frustrated $S=1/2$ models with competing antiferromagnetic interactions. Our scheme uses the basis of total spin eigenstates of clusters of spins to avoid the severe sign problem faced by other QMC methods. We also flag important limitations of the new method, and comment on possibilities for further progress.Comment: 6 pages + appendix with supplemental informatio

A simple analytical description of the non-stationary dynamics in Ising spin systems

The analytical description of the dynamics in models with discrete variables (e.g. Isingspins) is a notoriously difficult problem, that can be tackled only undersome approximation.Recently a novel variational approach to solve the stationary dynamical regime has beenintroduced by Pelizzola [Eur. Phys. J. B, 86 (2013) 120], where simpleclosed equations arederived under mean-field approximations based on the cluster variational method. Here wepropose to use the same approximation based on the cluster variational method also for thenon-stationary regime, which has not been considered up to now within this framework. Wecheck the validity of this approximation in describing the non-stationary dynamical regime ofseveral Ising models defined on Erdos-R ́enyi random graphs: westudy ferromagnetic modelswith symmetric and partially asymmetric couplings, models with randomfields and also spinglass models. A comparison with the actual Glauber dynamics, solvednumerically, showsthat one of the two studied approximations (the so-called ‘diamond’approximation) providesvery accurate results in all the systems studied. Only for the spin glass models we find somesmall discrepancies in the very low temperature phase, probably due to the existence of alarge number of metastable states. Given the simplicity of the equations to be solved, webelieve the diamond approximation should be considered as the ‘minimalstandard’ in thedescription of the non-stationary regime of Ising-like models: any new method pretending toprovide a better approximate description to the dynamics of Ising-like models should performat least as good as the diamond approximation

Data clustering using a model granular magnet

We present a new approach to clustering, based on the physical properties of an inhomogeneous ferromagnet. No assumption is made regarding the underlying distribution of the data. We assign a Potts spin to each data point and introduce an interaction between neighboring points, whose strength is a decreasing function of the distance between the neighbors. This magnetic system exhibits three phases. At very low temperatures it is completely ordered; all spins are aligned. At very high temperatures the system does not exhibit any ordering and in an intermediate regime clusters of relatively strongly coupled spins become ordered, whereas different clusters remain uncorrelated. This intermediate phase is identified by a jump in the order parameters. The spin-spin correlation function is used to partition the spins and the corresponding data points into clusters. We demonstrate on three synthetic and three real data sets how the method works. Detailed comparison to the performance of other techniques clearly indicates the relative success of our method.Comment: 46 pages, postscript, 15 ps figures include

Magnetization processes of irregular dendrite structures - a Monte Carlo study

The paper refers to micromagnetic simulations of magnetization processes of dendrite-like object. The objects were generated by the DLA fractal algorithm that allows obtaining fractals with different ratio of the spins attributed to the surface to volume. The simulations were carried out using the cluster Monte Carlo algorithm designed for spin continuous and multiphase magnetic systems. The presented researches include different magnetic anisotropy of the surface and volume reflected magnetically soft, hard and ultra-high coercive phases. As it was shown, the influence of microstructure on the coercivity mechanism is a complex phenomenon. In the case of the fractals with magnetically soft volume the increasing surface contribution causes either increse or decrease of the coercive field for relatively high or low magnetic anisotropy of the surface, respectively. For the fractals with ultra-high coercive volume the occurrence of the surface anisotropy leads to the significant deterioration of their hard magnetic properties. The obtained spin configurations show that this effect is related to non-colinear directions of the surface anisoropy and strong enough exchange coupling between the surface and volume

Hybridization expansion impurity solver: General formulation and application to Kondo lattice and two-orbital models

A recently developed continuous time solver based on an expansion in hybridization about an exactly solved local limit is reformulated in a manner appropriate for general classes of quantum impurity models including spin exchange and pair hopping terms. The utility of the approach is demonstrated via applications to the dynamical mean field theory of the Kondo lattice and two-orbital models. The algorithm can handle low temperatures and strong couplings without encountering a sign problem.Comment: Published versio

Magnetic properties of polypyrrole - coated iron oxide nanoparticles

Iron oxide nanoparticles were prepared by sol -gel process. Insitu polymerization of pyrrole monomer in the presence of oxygen in iron oxide ethanol suspension resulted in a iron oxide - polypyrrole nanocomposite. The structure and magnetic properties were investigated for varying pyrrole concentrations. The presence of the gamma - iron oxide phase and polypyrrole were confirmed by XRD and FTIR respectively. Agglomeration was found to be comparatively much reduced for the coated samples, as shown by TEM. AC susceptibility measurements confirmed the superparamagnetic behaviour. Numerical simulations performed for an interacting model system are performed to estimate the anisotropy and compare favourably with experimental results.Comment: 11 pages,8 figure